Topologies of Organization: Space in Continuous Deformation

Introduction

Organization studies have witnessed several attempts to bring ‘space back into’ organization (Barinaga, 2017; Beyes & Steyaert, 2012; Dale & Burrell, 2007; Hydle, 2015; Kornberger & Clegg, 2004; Lamprou, 2017; Scott & Spicer, 2007; Spicer, 2006). Generally, these studies protest the assumption that space is a neutral container of activities and call for an exploration of its active part in the making of organization. Proposing that ‘organizations should be thought of as material, spatial ensembles’ provides Kornberger and Clegg (2004, p. 1095) with a distinctive way of exploring how power relations materialize in spatial arrangements and architectures. Other studies highlight the human embodiment, appropriation and contestation of space; human agency that challenges the intentions and designs built into architectures and workspaces (Dale, 2005). Considered through a nexus that emphasizes the inevitability of power-resistance, we find studies of the spatial performance of gender (Tyler & Cohen, 2010), social movements’ need of spaces free from surveillance and control (Haug, 2013), and the appropriation and personalization of space (Warren, 2008). In its most ambitious form, Taylor and Spicer (2007) offer an ‘integrated synthesis’ to explore the ‘multiplicity’ of organizational space and its dynamics of power-resistance across macro, meso and micro scales.

While difficult to integrate, these studies have mobilized a relational understanding of organizational spaces, emphasizing that organizational space is both generative of sociality and also itself subject to social processes (Dale & Burrell, 2007). At the same time, they have been criticized for compartmentalizing space into dichotomies (Beyes & Steyaert, 2012). This leads to a situation where scaling is reduced to a hierarchical conception that positions the macro against meso and micro levels (e.g. Taylor & Spicer, 2007). It also generates a pervasive dichotomy between ‘“cold calculation” of the conceived space . . . [and] the embodiment . . . of lived space’, with the effect of downplaying the processual emergence of space and its more-than-human agencies (Beyes & Steyaert, 2012, p. 49). Recently, however, we have also seen new attempts to approach organizational space as open-ended ‘spacing’ (Beyes & Steyaert, 2012), ‘unexpected becomings’ (Knox, O’Doherty, Vurdubakis, & Westrup, 2015, p. 1001), and as a result of ‘action in all its forms—human, textual, technological, and discursive’ (Vásquez & Cooren, 2013, p. 29). Such work helps us see the contingency of spatial hierarchy and therefore loosens the reification of power as a stable spatial distribution within organization. These contributions emphasize a performative and processual view where incompleteness and disorganization are internal to a continuous socio-material production of organizational space.

This paper contributes to this processual understanding of organizational space by conceptualizing it as topological and by examining how organization emerges across different topological figures in an empirical example. While gaining increasing importance across the social sciences, the concept of topology originates in mathematics and regards how objects become deformed and retain continuity in different spaces (Lury, Parisi, & Terranova, 2012). In this paper I suggest that topology compels us to explore organization as unfolding in different topological shapes, as an ongoing ‘process of figuration’ (Lash, 2012). Drawing on the insights of, among others, (post)-actor-network theorists (ANT) John Law and Vicky Singleton (Law, 2002; Law & Singleton, 2005), the paper empirically explores such mutability across different topological shapes.

The paper proceeds as follows. The next section reviews how space has been taken up in organization studies where there is a notable focus on the application of Lefebvre (Beyes & Steyaert, 2012; Giovannoni & Quattrone, 2018; Scott & Spicer, 2007). Building on and contributing to approaches that emphasize space as process, a theory section introduces topology as it is taken up in cultural theory and post-ANT (Law & Singleton, 2005; Lury et al., 2012; Marres, 2012). This provides insight into how we might theorize organizational space as something which is in constant topological deformation. The ensuing section introduces the empirical study and its methodology. The empirical part reports a qualitative study of Danish school managers where the method of shadowing was used and where ‘interruptions’ of management activities were a central finding (Mintzberg, 1990). Interruptions are here used as an empirical entry point to explore the unfolding topological deformation of organizational space. Juxtaposing a management meeting with its interruption, the empirical case allows engaging spatial deformation across different topological shapes as it happens (Knox, O’Doherty, Vurdubakis, & Westrup, 2015). In the concluding discussion, I draw out some important implications of a topological understanding of space: the abandonment of pre-established organizational scales and an understanding of dis/organization as a spatial phenomenon.

Space and Multiplicity in Organization Studies

Henri Lefebvre’s (1991) seminal work on the production of space has been widely taken up by organization scholars (Beyes & Steyaert, 2012; Dale, 2005; Giovannoni & Quattrone, 2018; Taylor & Spicer, 2007; Zhang & Spicer, 2014). Briefly, Lefebvre argues that space is the result of three distinct spatialities interfering with one another, namely, conceived, perceived and lived space (Giovannoni & Quattrone, 2018, p. 862). This spatial triad has been interpreted in a variety of ways. One interpretation conceives the triad as including a ‘multiplicity of spatial scales’ with three scales of organization: macro (planned), meso (conceived) and micro (lived) levels (Taylor & Spicer, 2007, p. 341). Relatedly, other interpretations use Lefebvre to understand the ‘spatial politics of organizational control’, highlighting the entwinement of managerial control and embodiment (Dale, 2005), or how ‘spatialized power relations are reproduced on a day-to-day basis’ (Zhang & Spicer, 2014, p. 739).

Space, in these literatures, materializes and maintains power relations, generating and reproducing ideological and hierarchical organizational realities. While I do not wish to question this claim, there is a risk that such studies enact a rather singular and inert version of space and thereby underestimate the complex and multiple ways in which power works in organization. Indeed, Beyes and Steyaert (2012, p. 49) observe a tendency in the applications of Lefebvre to ‘reify space, turn spatial becoming into representations of the beings of organizational spaces’. Others note how spatial analysis is restricted to framing the unfolding of spatial change within temporal and physical boundaries (Giovannoni & Quattrone, 2018, p. 864; Petani & Mengis, 2016). There is thus the risk that spatial becoming might emerge as manifestations of relations of dominance, overshadowing its more open-ended and dis/organizing properties (Knox et al., 2015).

Other scholars use Lefebvre’s spatial multiplicity to emphasize ‘spacing’ as a socio-material, affective and non-representational phenomenon, which is ‘performed through the simultaneous and excessive coming-together of multiple trajectories and forces’ (Beyes & Steyaert, 2012, p. 53). Giovannoni and Quattrone (2018) further develop this by exploring the role of ‘present absences’ to account for incoherence and oppositions in spatial organization (pp. 863, 865). Here, Lefebvre’s triad is used to explore the ‘dynamism’ and ‘excessive coming-together’ of spatial becoming, leaving the spatial outcome open-ended and incomplete.

Also, scholars associated with the communicative constitution of organization (CCO) have long addressed the communicative and socio-material processes constituting organization (Brummans, Cooren, Robichaud, & Taylor, 2014). They have expanded this approach to include the communicative constitution of organizational space, proposing ‘the construct of multiple and heterogeneous sociomaterial interrelations, which coexist and affect each other’ as their definition of space (Vásquez & Cooren, 2013, p. 27). They identify space as central in materializing organization, in distributing and relating actors, as well as in constructing coherence across different times and places. Multiplicity here regards a plurality of ‘dis-local’, socio-material trajectories that need communicative coordination and accounting, concluding that ‘a multiple and fragmented space needs to be assembled in the singularity of a “we”’ (Vásquez & Cooren, 2013, p. 42).

While the socio-material and processual achievement of organization is also central to Knox et al. (2008, 2015), they emphasize dis/organization as integral to the multiplicity of space: ‘The disruptions of the un-usual and the un-expected makes airport spaces appear less and less as “containers” . . . and more and more as enactments: spacings’ (Knox et al., 2015, p. 1007). Space can at once be ‘“backgrounded” in the repetitive and pragmatic routines of organization’ and ‘“return” as problematic’ when new relations to other spaces, agencies and materials emerge (Knox et al., 2015, p. 1007). Here, multiplicity regards how space is interlinked with organization/disorganization. We thus see many scholars emphasizing the relationality and multiplicity of space, either in terms of multiple and intersecting spatial scales, multiple and excessive trajectories and forces, and dis/organizing enactments of space. Below, I suggest that the concept of topology adds to these an understanding of organizational space as in constant deformation across multiple topological figures or shapes.

Topology: Space in Continuous Deformation

Across the social and cultural sciences, there is a growing interest in the concept of topology to address the mutability and relationality of space (Brown, 2012; Gulson & Sellar, 2018; Hetherington, 1997; Lash, 2012; Law, 1999; Lury, 2013; Marres, 2012; O’Doherty, 2013). A mathematical concept, topology has emerged in response to ‘the perceived rigidities of geometric shapes and surfaces that take their cue from the clearcut coordinates of Euclidean space’ (Allen in Gulson & Sellar, 2018, p. 4). Central in topology is thus an understanding of space (and time) as emergent becomings rather than a priori categories. In that sense, a topological approach fits well within existing discussions about the relationality and open-ended nature of organizational space outlined above, extending to non-representational theory, post-ANT and urban geography (Law, 1999; Massey, 2005; Thrift, 2008).

Topology offers a particular take on what spatial becoming might mean: we see space as in ‘continuous deformation’, which means that dis/continuities and surface relations between different agencies morph (Lury, 2013). Surface relations, here, should not be understood in dualistic comparison to depth relations. Rather, with a topological approach, surface relations are all we have; everything happens on the same plane (cf. Deleuze & Guattari, 1980; Latour, 1991). This leads us to think of space as something which is continually curving and deforming. As Hetherington argues, ‘topology is concerned with what happens when a space, a bit like a sheet of rubber, is folded, twisted and distorted in a variety of different ways while retaining its overall properties as a space’ (Hetherington, 1997, p. 199). Topology, thus, is a way to extrapolate how organizational space can take up multiple shapes. These shapes are not ‘fixed by way of external co-ordinates but . . . organized from within’ (Lury et al., 2012, p. 7). This view of organizational space as a matter of changing surface relations thus compels us to explore how relationships between inside/outside, near/distant, present/absent, dis/continuous, order/disorder are immanent to space itself. This implies that ‘invariance and intrinsic change (understood as deformation) are not incompatible; rather rigorously inter-related’ (Lury et al., 2012, p. 7). With topology, thus, changing surface relations in fact entail the continuity of organizational space which morphs across different topological shapes.

Attention to how space topologically deforms is important when we are interested in the processual, heterogeneous and laboursome work needed to stabilize and enact organization as a singular entity. It allows us to follow and explore the interdependencies of different human and non-human agencies in assembling and mobilizing organization. When relations between these agencies change, such topological figuration may interfere with actors’ possibilities for narratively enacting and making sense of organization. As we will see in the empirical sections of this paper, topological figuration is interrelated with whether managers background space or make it an object of inquiry. Topological figuration of organizational space can generate possibilities of narratively enacting futures, but also situates managers’ bodies in an intense present where their ‘stories about the world fail’ (Munro & Belova, 2008, p. 87). Topological deformation of organizational space, thus, is also deeply interdependent with different constitutions of organizational time, in terms of managers’ possibilities of narratively enacting pasts and futures (cf. Jones, McLean, & Quattrone, 2004; Latour, 1997). In the analysis I will pay attention to this relationship by looking at how different topological figurations of organizational space produce different conditions for managerial narratives to tame and stabilize organization. ¹

Now, how to explore this empirically? While there are many different socio-cultural take-ups of topology, my approach is inspired from, but not limited to, the way Law and Singleton have used it (Law, 1999; Law & Singleton, 2005; Mol & Law, 2002). ANT is by now well-known in processual and socio-material approaches to organizing (Cooren, 2006; Czarniawska & Hernes, 2005; Latour, 2013; Law, 1994) and has already been put to work in analysing the heterogeneous ‘process of building organizational agency and remaking space’ (Barinaga, 2017; see also Jones et al., 2004). Emphasizing multiplicity and mess, post-ANT speaks well to ongoing discussions in organization studies about the emergent and dis/organizing making of spaces (Barinaga, 2017; Cooren, 2006; Giovannoni & Quattrone, 2018; Jones et al., 2004; Knox et al., 2008, 2015). Post-ANT introduces the idea of topological multiplicity as a sympathetic critique of the trope of the network and its topological presuppositions of stability and powerful enrolments (Brown & Reavey, 2017; de Laet & Mol, 2000; Law & Singleton, 2005; Mol & Law, 2002). Topology, with its focus on changing surface relations and dis/continuities, brings spatial imagination beyond that of the network.

With what they call (inter alia) ‘fluid’ and ‘fire’ topologies, we are invited to explore the emergence of space without granting analytical primacy to durable networks upheld by ‘immutable mobiles’ (Law, 1999; Law & Singleton, 2005; Mol & Law, 2002). As especially the concept of immutable mobiles has been taken up to explore the socio-material and processual constitution of organization (Cooren, 2006; Cooren & Fairhurst, 2009; Cooren, Matte, Taylor, & Vasquez, 2007), at the cost of dis/organization, the intervention offered by post-ANT is also warranted in organization studies. I thus propose that the different topological figures suggested by post-ANT are helpful for navigating the topologically shifting shapes of organizational space in a situation where objects and humans may be dis/associated in ways that result in changing relations between inside/outside and distant/near. ²

After-Method: Enacting Topological Deformation Through Shadowing

Scholars have suggested that it is necessary to study the making of organizational space as it happens (Beyes & Steyaert, 2012; Knox et al., 2015). At the same time, we might well characterize organizational topologies as ‘elusive realities’ that ‘exceed our capacity to know them’ (Law, 2004, p. 6). This means that any methodological entry point most likely will exclude as much as it enacts. My choice of term, ‘enacted’ rather than ‘represented’, situates this study as an ‘after method’ approach (Law, 2004). Rather than using methods to ‘obtain the best and technically robust possible account of reality’, an idea that presumes reality as a ‘set of possibly discoverable processes’ (Law, 2004, p. 9), ‘after method’ understands methods as performative: that is, rather than representing a pre-existing reality, methods contribute to the making of those very realities. This means that this study itself constitutes a spatial practice of ordering (Law & Singleton, 2005; Lury et al., 2012). Empirically capturing and analysing the topological deformation of organizational space, thus, also enacts, stabilizes and dramatizes organizational topologies in a contingent way. It is against this backdrop that I intend the following to be read.

The empirical examples are taken from a qualitative study of two Danish municipal primary and lower secondary schools conducted in the period 2009 to 2011. The study explored the performance of school management and organization in everyday practices. It mainly made use of the method of ‘shadowing’ (36 full days), ³ an approach termed one of the most ‘promising methodologies’ to explore the ongoing constitution of organization (Schoeneborn et al., 2014, p. 301). Specifically, eight managers (four at each school) were shadowed. With the exception of one, all had a teaching background. While the choice of shadowing draws upon the famous ANT dictum to ‘follow the actor’ (Latour, 2005), it is more closely affiliated with ethnographer Harry Wolcott’s (2003) study of one school manager. Following managers’ movements across different physical locations is particularly fruitful for understanding the relationship between space and organizing. It allows the tracing of how heterogeneous agencies produce continuities between places and domains that are usually considered to be separate (Czarniawska, 2008).

During shadowing, I looked for agencies (human and non-human) that contributed to or challenged processes of organizing and managing (Latour, 2013; Vásquez & Cooren, 2013). Spreading the 36 days over two years provided information about the organizing effects of season-contingent events (such as welcoming new students to the school or writing up the annual quality assessment report). The timespan further had the effect of moving analytically and physically between ‘field’ and ‘desk’ where each offered ‘a perspective on the other’ (Strathern, 1999, p. 1). I used this analytical back-and-forth movement to strategically redirect my attention to focus on aspects that I had missed in my notes from the perspective of the desk (e.g. the role of documents at a meeting), and conversely, resituating myself in the field, would often generally ‘interrupt’ the sense-making that had taken place at the desk.

Shadowing produced handwritten and computer-typed field notes (at meetings) as well as audio recordings of meetings. All were converted into computer-typed field notes. When both audio recordings and field notes were in use, I focused my note-taking on agencies of humans and non-humans (e.g. how documents circulated), to account for the ‘hybrid agency’ of organizing (Cooren, 2006). Shadowing moreover involves frequent dialogical exchange between shadower and shadowee where ‘mutually shared meanings are collaboratively and communicatively achieved’ (Quinlan, 2008, p. 1491). I recorded those casual conversations and transcribed and inscribed my own presence into the field notes. Shadowing produced an average of 15 computer-typed pages of field notes per day.

I coded and organized the field notes in a spreadsheet database, using coding strategies known from grounded theory (Corbin & Strauss, 2008). I used descriptive/topic coding, i.e. open-ended categorizations of ‘what was happening’, in-vivo coding which highlighted the participants’ own terms, and process-coding, which detailed the observed activities, with a focus on how (non)human agencies de/stabilized a situation or interaction (Saldaña, 2013). ‘Interruptions of planned activities’, coded with reference to school managers’ sense of being interrupted, emerged as one central theme here and I increasingly gathered data in my field notes under its title. Although I did not plan from the outset to engage with space or topology to analyse this data, the idea emerged when trying to make theoretical sense of such interruptions.

At both schools, managers reported that they have to intervene in unforeseen events two to four times a day. Sometimes these were handled in 15 minutes, other times they spilled into the entire day. While most days were fast-paced, turbulent and unpredictable in terms of the quantity and nature of these incidents, they were also an expected part of everyday life. Like Knox et al. (2008, p. 874), I found that the school principals would frequently talk about unexpected crises. As one put it in an interview:

On the surface it may seem calm but it takes so little for anything to break out with the vulnerable children. They are easily enrolled in trouble and chaos lurks just around the corner. You can feel it, just walking into a classroom . . ., vibrating, waiting for an occasion to break loose. (December, 2009)

In the following sections, I analyse a meeting that was perceived by staff members as being interrupted. When exploring the topological deformation of organizational space, interruptions are analytically interesting. As a relational phenomenon, interruptions only exist insofar there is an ordering or arrangement to which ‘something’ can appear as an interruption (Munro, 2001). Yet, as the analysis will show, interruptions challenge the distinctions between inside/outside and render visible the mutability and fragility of organizational space. While the empirical example used in this paper may be somewhat spectacular, it is important to emphasize that interruptions are neither ‘exceptional’ nor a phenomenon pertaining in particular to schools. Rather, they are a mundane and expected part of management (Mintzberg, 1990). Having an ‘extreme’ and quite literal case of interruptions (Flyvbjerg, 2006) dramatizes their effects and is helpful in eliciting this paper’s more general theoretical claim about the topological deformation of organizational space. ⁴

On a reflexive point, that interruptions emerged as a central theme also speaks to my ethnographic experience of managers not being faithful to their calendars. Such incidents changed their priorities and moved them around the school's property, to solve trouble at the playground or in a class corridor. My field notes reflect how managers postponed or cancelled meetings, writing assignments, and other planned activities when sudden events moved their bodies and attention. Analogous to the managers I shadowed, the interruptions made me move around the school at a pace that made it difficult to produce ‘complete’ descriptions of what happened. Interruptions left traces in my work in the form of fragmented field notes and a surplus of leads to follow. The topological deformation of space, thus, was not only something to be analysed but posed practical and narrative challenges for me during shadowing, writing up and coding field notes.

Network Topology: Enacting a Regional Space

In this section, I investigate the topology of a management meeting by looking at how human and non-human agencies produce particular surface relations between far/near. I will propose that the organizational space depicted here takes the, by ANT scholar’s well-known, topological shape of a ‘network’. A network topology allows for a relatively stabilized and well-aligned space that appears as a region with clear-cut boundaries (Law & Singleton, 2005). Now, let us enter the meeting. It has just started.

As is customary, the weekly management meeting takes place in the school principal’s office. Teachers and pupils are occupied in the classrooms and the secretary intercepts visiting parents and incoming phone calls. All four managers sit around a small table located next to the school principal’s desk. I have squeezed myself into the office corner next to the same table. The arrangement of people in the office, four managers and a shadower facing each other, allows the distribution of documents containing various kinds of information. We only need to glance at the printed agenda, of which we each have a copy, to anticipate the content of the two hours that the meeting has been scheduled. (Field notes, September 11, 2009)

This short depiction allows us to make two early observations. First, the space of the meeting is a result of associated and well-aligned humans and objects: The scheduling of the meeting coincides with teaching hours (as opposed to having it in one of the breaks where teachers frequently consult managers), the meeting agenda has been written and circulated a few days in advance. The secretary’s presence, the closed door, as well as managers being co-present allow for undisturbed interaction. Second, this space is not all-encompassing. It is also someone else’s unfolding interruption (the parents being interrupted by the closed door or the phone call being intercepted by the secretary, for example). This space is thus relative to the agencies producing the event of a meeting. As I will suggest in the following, this allows for a network topology with its own spatiality.

The closed door allows the conversation to be held in a confidential tone. The school principal goes through a stack of papers. Most of them do not become an object of discussion. Some are mentioned just to check if everybody has read them. Sometimes he stops and takes out single pages and discusses them in detail. They go through the annual ‘quality report’, discussing how best to word their efforts with inclusion of children with special needs to the municipal administration. They look at new legislation from the Ministry of Education and information from the municipality. These ‘agenda items’ are dealt with through utterances such as: ‘I have sent out information about the changes in school legislation to the union representatives. There are changes in the municipal reading plans and there is an integration of the pupil plan and the education plan.’ (Field notes, September 11, 2009)

The documents contribute to the stability and rhythm of the meeting. The stack of documents shrinks as papers are distributed to whoever takes the responsibility for following up on a given topic. Hernes, Bakken and Olsen claim that ‘organization is essentially about [the processual] stabilization of actions and expectations’ (2006, p. 46). The choreography around the documents produces such stabilized organizational space where the distribution of the tasks, as made present by documents, emerges as an unproblematic managerial function.

Here we see how the meeting space is produced through documents, which also connect the school to topographically distant places. Such connections topologically figures the meeting space in the shape of a network. The information about new legislation, for example, originates from the Ministry of Education. The agendas of topographically distant places, the ministry and local government, are made present in the meeting, rendering the managers’ interaction ‘dis-local’ (Cooren & Fairhurst, 2009). Verbal utterances also contribute to the making of a network spatiality. For instance, the alignment between ‘dis-local’ legislation and teachers is achieved through the verbal mobilization of the absent union representatives. The utterance that the union representatives have received the information enacts them as willing to distribute it further down the hierarchy. However, as Michel Callon reminds us, this is no guarantee of alignment as the ‘consensus and the alliances which it implies can be contested at any moment’ (1986, p. 15). However, the manager’s utterance renders absent this contingency and performs the implementation of the new legislation as an unproblematic future, allowing them to move on to the next item on the agenda. Here we thus see how a network topology allows the spatial constitution of the school as a stabilized and routinized organization. The managers mobilize and enact the organization through their interaction. At the same time, their agency is shaped by the documents, procedures and interests from other places, over which they have little control. In the following, I explore another spatial effect of the network topology: its possibility for the narrative enactment of futures:

(Field notes, September 11, 2009)

We can see here how the network topology separates time and space. The managers can enact the future as something to be anticipated and planned. Such communication is key ‘in distributing and relating actors, actions, means, and goals in time and space’ (Vásquez & Cooren, 2013, p. 41). The enactment of the future takes place through the association of speech and the schedule overview provided on the computer screen, the digitalized schedule being a ‘center of calculation’, an accumulation of inscriptions that can re-present absent teachers (Latour, 1987). As Law (2002) notes, ‘network spatiality produces and depends on such network-objects, objects which secure their constancy in a syntax of consistent functionality’ (p. 101). There is a recursive relationship between objects and space here. Whereas the schedule allows for ‘maintaining a certain sense of coherence’ (Vásquez & Cooren, 2013, p. 40), this schedule is itself a spatial achievement of network-building, a ‘black box’ (Latour, 1987) dependent on software, hardware and modern ideas of time and planning. Actions such as the deputy’s note-taking are also crucial. At the meeting, the note works as a placeholder for the future action of changing the schedule. Following Annelise Riles (2010), ‘one creates a placeholder in order to overlook it for the moment . . . it is a technique for working with the meantime . . . a tool of forgetting, of putting to one side’ (p. 803). In this way, the note-taking performs the expectation that the deputy will do this in a near future space. This allows the meeting to move on.

The enrolment and alignment of humans and objects produce a space that makes possible the event of a meeting. The network topology enacts the geographical space as a neutral container of people and documents. The specific location of the meeting fades into the background and is not an object of attention. It is present as a non-visible structure, allowing for connections to the municipality and the Ministry of Education, mediated by documents, but also disconnections from the local interactions at the school. Here we see how what is near and far is not determined by Euclidean coordinates but by contingent topological surface relations. We also see how a network topology enacts strong boundaries in time and space. With these in place, it only takes an utterance for the managers to jump between the staff meeting planned for next week and a document containing their budget. They can distribute tasks such as the planning of substitutes and attend to future issues such as when to arrange meetings with teachers. In a network topology, thus, human agencies have a relatively strong narrative power. It allows them to enact future actions and the future implementation of new legislation. The network topology, as Vásquez and Cooren (2013, p. 38) put it, allows managers to narratively construct a ‘place-moment for [future] actions to unfold’.

A missing document or a ball breaking the glass of the window, however, may challenge this topological shaping of space and its narrative generosity. Then, in contrast to the meeting just analysed, there would be no smooth passage of the agenda items, and the managers would be required to attend to the physical space in which their bodies are located. This reminds us that topological spatiality is a provisionary and fragile achievement. It takes very little to undo the partial detachment afforded by a closed door, and the meeting agenda can always rapidly lose its authorizing power. When the meeting is interrupted, as I will illustrate in the following, we see a topological change: space morphs, continuities are broken, and the boundary between inside/outside is suspended.

Suspending the Boundary: Topological Irruption of Organizational Space

In this section, I explore how an interruption undoes the network topology by imposing new dis/continuities. My account continues where we left the meeting. I will suggest that we understand this change as an irruption of organizational space. The school’s janitor knocks on the closed door separating the meeting from the world outside. He brings a complaint from the housing association next door. Some children, suspected to belong to the school, are trespassing on their property, riding a moped. The managers (and the shadower) get up and leave the office to find the children.

We move quickly, crossing the street right outside the school gate. We do not use the pedestrian crossing only 20 metres away, even if this is customary for all staff in order to set a ‘good example’. The once white, now gray, concrete buildings stand rather tall and faceless in front of us. The children are nowhere to be seen. We divide into two groups. The pace is fast and we move along the edges of the housing community, as if that could stop the children from escaping its hopelessly big area. One manager tells me how she hopes that they find the children quickly and that it is difficult for them to control what they do outside the school’s property. Apart from that, there is little talking. We look at the green strips of grass between the housing blocks as we walk along the pavement, bordering the area. We can neither see nor hear the children and the sense of urgency grows with our accelerated pace. As shadower, I also become uncertain of my own role. Should I step out of character in case they need an extra hand in handling whatever situation emerges? (Field notes, September 11, 2009)

This transition from the meeting marks a rather radical topological deformation of space. Rather than assuming the boundary between school and environment to be operating, the boundary has become a topic of anxiety for both the managers and the shadower. Before information such as ‘which children’ and ‘what has happened’ is elicited, the interruption first and foremost produces non-knowledge. The managers do not know exactly what is going on or whether indeed it is a problem to which they should respond as managers. What are the pupils doing with the moped at the neighbour’s property? Have any buildings been vandalized? Have any residents become upset? Are there other elements involved than a moped? Is it, indeed, the school’s problem at all? Perhaps the children are not pupils of the school. The interruption renders the managers’ bodies ‘out of place’ and also ‘out of narrative’ (Munro & Belova, 2008, p. 97).

We might understand the managers’ movement on the pavement as a change in topological surface relations. In contrast to the meeting where the office space withdraws into the background, the managers here pay intense attention to the immediate space, searching for the children. Whereas the network topology allowed for making present other times and places, the managers (and the shadower) have little possibility of narratively enacting pasts or futures. The space of the meeting, with its connections to the ministry and local government, has here shrunk to the point of its non-existence. Instead, the school expands its spatial operations to include streets, pavements and housing blocks. Formerly insignificant, these become large and a matter of concern. The managers become temporarily defined by this uncertainty, anticipating the breaking down of order (Brown & Reavey, 2017).

These uncertainties illustrate how the narrative production of ‘problems’ to be managed is spatial. In contrary to the meeting, objects and space can neither be backgrounded nor be emplaced in a narrative order in this situation. Latour (1997) notes that ‘the separation between time and space . . . is not a fundamental distinction’ but a result of (non-)human actors doing their ‘timing’ and ‘spacing’ (p. 176). The fabrication of time and space in this situation is very different to the one we saw in the meeting, ‘to the point of one [non-separated] timespace’ (Latour, 1997, p. 176). In contrast to the proposition that space can be communicatively assembled and configured (Vásquez & Cooren, 2013), organization may also be spaced in topological figurations that negate such narrative possibility. In this way, the janitor thus heralds both an interruption of narrative (Munro & Belova, 2008) and an irruption of space.

We see here how spaces are simultaneously large and small, depending on relational configuration, the surfaces to which they are made to connect, and how these surface relations result in different topological shapes. Discussing how organizational space changes when ‘something happens’, Knox and colleagues note:

Space intrudes as a problem to be negotiated - a figure of anxiety. During moments of uncertainty, participants - including ourselves - are reminded of the contingency of spacings as we become increasingly aware of the multiplicity and mutability of spaces that are routinely normalized and ‘backgrounded’ in the repetitive and pragmatic routines of organization. (Knox et al., 2015, p. 7)

The topological deformation emerging with the janitor’s interruption renders space visible as unknown and uncertain, and neither the school’s concrete walls nor the printed meeting agenda can delimit the managers’ attention and movement.

In this situation, it is difficult to tell where the school ends and where its environment begins. Cooren and Fairhurst (2009) suggest that organizational space is produced by walls, gates and other enclosures, delegated with the task of delimiting ‘who is in and who is outside the building’ (p. 140). An irruption in the topological space, it seems, undoes this work and makes us realize that even walls and gates are situational achievements. Brown and Reavey (2017, p. 86) characterize such dis/continuities as ‘breach space’: ‘The boundary is nothing and nowhere, until it is revealed through the act of breach. And then it envelops you.’ In the example analyzed here, the suspension of the boundary is not simply a theoretical problem but a very practical problem for the school managers to handle.

So how do these moments of deformation differ spatially from the network topology? While the network topology enacted organization as a bounded regional space, this ‘breach’ space suspends such orderings and boundaries. The breach space further grants the managers little narrative possibility of enacting pasts and futures – their narrative has been interrupted. Paraphrasing O’Doherty, such radical topological deformation, or spatial irruption, entails ‘access to a dimension of being that is caught outside or between the recursive loops of narrative and meaning awaiting a moment of singularity around which a phase transition or transformation from one spatial pattern to an as yet unknown shape might take place’ (O’Doherty, 2013, p. 213). This results in the anticipation of breakdown and one momentarily cuts connections to dis-local orderings from the Ministry of Education, the digital school schedules and other powerful ‘centres of calculation’ (cf. Latour, 1987).

Fire Topology: Spatial Inclusion of Absence-Presences

Eventually we find six older boys and a younger one, all pupils of the school. The younger one is temporarily suspended from school due to a recent violent incident. He should be at home now. The older pupils are also familiar faces as they have a history of bullying the suspended boy. They should be in class now. The boys walk with a moped, which I assume to be stolen. It has been spray-painted white, but the original colours shine through and short-circuited wires stick out from the dashboard. The air is thick with suspicion, the gravity of the situation illustrated by the presence of the entire management team. Before any questions are asked, the boys claim their innocence. One gets a soda from the box beneath the moped’s seat and drops the bottle top on the ground. A manager picks it up but does not say anything. Another manager asks them what they are doing here, motivating different versions of the same reply: ‘I didn’t drive the moped, I didn’t do anything, it wasn’t me.’ Meanwhile, a manager has taken a step back to call the police who he involves in petty crimes as a preventive measure. At this moment, however, the police are busy and unable to assist. We stand at the spot for some time and it seems that no one knows what to do next since the police cannot come. The boys continue to deny that they have been riding the moped (still without this accusation having been made) and another manager talks to the housing association representative who has also turned up. A manager who has been deeply involved in past conflicts with the suspended boy takes him to her office (and I follow along). We sit down at the table and the boy is now eager to talk to the manager, in contrast to his quiet behaviour in front of the older pupils. He tells us that he uses the moped to deliver marijuana from a local drug dealer who sits at a bench between two neighbouring apartment blocks. During this activity, he bumped into the older pupils. They took the moped to tease him, he tells us, and expresses his fear of them (‘They want to smash me up. I don’t want to go out to them. Please let me wait for the police here, with you’). He seems to be surprised that the manager does not know of the drug dealer (‘seriously, you don’t know about this? But everybody knows he’s there’). (Field notes, September 11, 2009)

That the managers find the children and recognize them as pupils of the school, I will suggest, results in a new topological deformation of organizational space. Rather than the non-knowledge of an emerging crisis, and its breach space, they are confronted with matters they can identify as ‘management problems’: truant pupils, a suspended pupil, a stolen moped, a drug dealer, an unhappy neighbour. The spatial irruption analyzed in the previous section resulted from the association of these elements, a ‘parasitic cascade [where] one act of interception is interrupted by a further act’ (Brown & Reavey, 2017, p. 291). Yet, once identified by the managers, they allow a narrative ordering of the event.

This, however, does not mean that organization spatially is reconfigured into the network topology. The interruption and irruption have (re)connected the school to neighbouring realities that were otherwise ignored or actively being excluded from the meeting. When dealing with ‘the interruption’, which is now transformed into a plurality of ‘problems’, the managers cannot fully control which problems belong to the school and which do not. Stolen mopeds become associated with the school, even if theft falls under the jurisdiction of the police. When the police are busy elsewhere, however, the school managers need to do their (police) work. The suspended boy falls under the legal responsibility of his parents but ends in the office of one of the school managers. The parents cannot be reached by phone. The drug dealer is not only a matter for the police but is also seen as a risk for the school’s other pupils, especially given how ‘everybody knows he’s there’. Small details (a boy suspended from school, taken care of on a different day) end up being the most crucial challenge of the day, folding in a range of problems that do not officially belong to the school. As a result, we can no longer count on a network spatiality that make humans and objects faithful to a meeting agenda, rehearsing and maintaining hierarchical relations from the Ministry of Education to the school.

Instead, we might interpret organizational space here as taking on the topological shape of what Law and Singleton (2005) refer to as fire. A fire topology is characterized by the re-emergence of elements that have been excluded from a network spatiality and so undoes its dis/continuities (Law & Singleton, 2005, p. 342). Fires are ‘energetic and transformative’ and ‘depend upon otherness [which is] generative’ (Law & Singleton, 2005, p. 344). The police, parents, stolen moped and drug dealer are all ‘organizationally other’ (p. 344) to the school, yet the spatial irruption makes them organizationally present as problems to be handled. This inclusion, however, is generated in juxtaposition with absent realities (p. 345): the absence of police, parents, and not least an absent solution in relation to handling the next door drug dealer. Figured as a fire topology, organizational space is generated as a series of absent-presences: matters of concern which are at once spatially situated in and spatially disconnected from the school.

Compared to the topology of breach space, which suspended all boundaries and situated managers outside narrative sense-making, a fire topology does not exclude managerial narrative. Yet, narrative sense-making has very different conditions than when performed in a network spatiality. The managers cannot plan the future as they did during the meeting. They can, for instance, neither anticipate when the police will arrive, whether the police will catch the drug dealer, nor when they can get hold of the suspended boy’s parents. The possibility for spacing time, in a fire topology, is fraught with anticipated breakdowns and unknowns.

In one respect, the fire topology is the flipside of the network topology, introducing elements that have been excluded from the socio-material space of the meeting. It stands in a relational contrast to the network topology. However, it is not simply a reversal of the network topology, with reversed surface relations and opposite pattern of absences and presences; this would assume a fixed number of entities that could be included/excluded. There is a difference in scale, in the number of entities associated, a difference, as it were, in how space is crumpled (Hetherington, 1997). With the topological irruption constituted by the breach space, we saw a growing number of actors (bullying pupils, suspended pupil, drug dealer, etc.) attached to the situation. This reveals an underlying topological multiplicity that is singularized during meetings. The irruption generated an encounter with such Othered multiplicity. When morphing into a fire topology, these agencies become spatially (re)attached to organizational space, and this at a relentless pace that calls for the managers’ immediate response. The mutability of space thus produces interrelatedness, by including Othered agencies, connecting points that used to be far apart.

Topology’s sensitivity to the dynamic potential and shape-shifting effects of such dis/continuities reminds us that the narrative interruption is only an interruption in relation to the meeting’s spatial production of organization. The boy’s account of ‘what happened’ reveals a multidimensionality of space. Indeed, the suspended boy was surprised that the managers did not know of the drug dealer next door (‘but everybody knows he’s there’). This indicates that the boundary between school and its environment is topologically relative to which person one talks to, to the spaces they inhabit. It does not take effect for all actors at the school. If the analytical starting point were a different ordering, then the narrative interruption would be different, too (cf. Knox et al., 2015, p. 1014). For instance, one could have explored how the management team interrupts truant pupils’ bullying of the suspended kid – they can no longer go on with their teasing and violence. The truant pupils, in turn, interrupt the suspended pupil’s activities of assisting with drug dealing. The police and parents interrupt an ‘organizational script’ (cf. Latour, 2013) by not being available when needed. In such ways, spatial productions of dis/order are topologically relative to the different actors cohabitating the same territory, revealing the multidimensionality of a topologically curving space (Lury et al., 2012, p. 21).

Conclusion: The Constant Topological Deformation of Organization

This paper has aimed to develop theory in organization studies by way of the concept of topology and an empirical enquiry into space as being in constant deformation. Topology posits ‘constant deformation’ as the norm, involving changing surface relations that will always result in different dis/continuities and different spatial shapes, and whose emergence surprises us by the extent to which we are still Euclidean in our thinking and practice of organization. To navigate shifting topological forms of organizational space, the paper has taken its inspiration from Law and Singleton’s topological metaphors of network and fire, as well as O’Doherty’s (2013) and Brown and Reavey’s (2017) theorizations of intersecting spaces. With these resources we can help open up for enquiry those moments of a topologically shifting organizational space, where the furniture of everyday organizational life is moved around – by design or by accident. This further opens up a space (or rather ‘spacings’, for all appears in movement at this point) or void that can only be described as existing somehow before meaning and thereby awaiting narrative order.

Conceptualizing organizational space as constantly curving, or as in constant deformation, involves two advances in current organizational thinking about space. First, it breaks with the idea that organization happens at pre-established spatial scales, forcing us to abandon the analytical scaling of space into hierarchically nested micro, meso and macro levels, as some interpretations of Lefebvre have suggested (Taylor & Spicer, 2007). Space and scale, instead, are a result of socio-material agencies in constant (re-)enactment, mediation and re-figuration (Jones et al., 2004; Latour, 1997). With topology, we see organizational space as the emergent effect of socio-material agencies whose dis/continuities take different topological shapes. These shapes may sometimes enact hierarchical power relations as we saw in the meeting. Yet, in spite of ‘immutable mobiles’ and the school’s architectural temporal-spatial disciplining of pupil-bodies in classrooms at fixed times (for some in organization studies, a Foucauldian disciplining), it is in fact a fragile spatial arrangement.

Not only does this entail implications for the popular take-up of Lefebvre in organization studies that interprets spatial analytics in the relatively simple terms of power-resistance - where power is inscribed into and works through architecture. In addition, we must also try to think of organizational space as something which is a situational achievement that operates outside the existing powers and calculations of architects and designers. We cannot assume an a priori distinction between ‘lived’ space and its ‘objective’ or calculated properties. As we have seen, alongside others (Beyes & Steyaert, 2012; Latour, 1997), these spaces, boundaries and calculations break down. In this case, the actors have to operate with a sense of always being on the edge of immanent breakdown.

The empirical example has explored how buildings and office environments achieve their spatial effects through their interaction with a multitude of agencies that fold in ‘distant’ agendas. Appropriating and resisting space, further, are not left to humans but also involve objects such as stolen mopeds. This is not an argument against the ‘affordance’ of architecture; rather it is a call for exploring the spatial production of organization in situ, in its processual and emergent becoming (Knox et al., 2015). This calls for methods within ethnography, or other attempts at ‘slow-motioning’ (Beyes & Steyaert, 2012), that allow for exploring space as process with a sensitivity to more-than-human agencies (O’Doherty, 2017). When space appears singular and stable, e.g. during the meeting analysed, this is a result of socio-material agencies in alignment, successfully dis/connecting to other agencies. This spatial achievement, however, is fragile, and leads us to understand organization as a ‘precarious, even transient, condition’ (Knox et al., 2015, p. 1013).

Second, working with topology helps elicit what is a recursive relation between the spatial production of order and disorder: rather than being each other’s opposite, order is a socio-material, situated and relational achievement (Knox et al., 2015). This posits Cooper’s (1986) famous idea that organization and disorganization are mutually implied as a fundamentally spatial process. Interruptions are not, as is commonly understood, ‘external events disrupt[ing] the normal flow of organizational and relational routines and practices’ (Powley, 2009). Rather, they are internal to the collective performance of organization (Marres, 2012; Munro, 2001). They are ‘overflows’ or Otherness that spatially challenge and revise particular arrangements (Callon, 1999; Law & Singleton, 2005). The empirical example allowed us to access how a simple interruption in fact was a ‘parasitic cascade [of] interceptions without a clear stopping rule’ (Brown & Reavey, 2017, p. 291), which generated a spatial irruption and unravelled the provisional spatial boundary between school and environment. Different topologies are thus recursively related: without the network spatiality of the management meeting there would be no absent-present fire topology to overwhelm the school management with excluded worlds and orderings. Working with a topological notion of spatial becoming, thus, sharpens the analytical gaze towards the multiple topologies through which space ‘combines order and chaos; it embodies (dis)organization’ (Kornberger & Clegg, 2004, p. 1105).

Topology thus points to spatial mutability, and allows us to explore how surface relations between distant/near, inside/outside, present/absent unfold and transform (Lury et al., 2012; Ruppert, 2012). As witnessed, the narrative mobilization of organization is contingent upon whether boundaries and scales are kept in place, such as the boundary work that is constantly enacted to try and separate problems which belong and problems which do not belong to an organization. Organizing, thus, cannot be separated from the topological shaping of space; different topologies of organization condition what can become a matter of concern for management.

Working on wider sociological fields of enquiry, Lury et al. (2012) have suggested that ‘culture’ is becoming topological. I want to suggest here that organization is always-already topological even though we might be said to exist these days in a culture of topology, or a topological culture. This is by virtue of specific concerns of organizational studies, such as how we might understand space as processual, emergent and multiple. Once we understand space as changing surface relations, we can see how these changes may be subtle and undramatic, as in the meeting where centres and peripheries and various futures are unproblematically enacted on a continuous basis. Or they may be dramatic, as with the interruption, morphing organizational space as a breach (Brown & Reavey, 2017), in passing to the immanence of fire topology.

In engaging the concept of topology to elicit the unfolding spatial deformation of a Danish school, this paper suggests that topology offers important insights to existing socio-material, relational and processual explorations of organizational space. While socio-material process studies of organizational space in different ways argue that space is spacing (Beyes & Steyaert, 2012; Giovannoni & Quattrone, 2018; Jones et al., 2004; Knox et al., 2015), topology helps us tune into those moments of change, and their consequences for organizational and temporal narration, through its attention to changing surface relations. Blok (2010, p. 910) argues that we ‘should entertain the notion of a potentially endless number of topological shapes, overflowing also our own analytical categories’. This calls for an open-ended attitude where we as scholars invite socio-material organizational realities to shape how we conceptualize them, in the work of extrapolating and enacting new topologies of organization.