Cross-fertilizing knowledge, translation, and topologies: learning from urban housing policies for policy mobility studies

. Recently, urban housing policies in Europe have become more mobile, developing local responses to the housing question by building on examples from other cities. To understand the movement of policies, the policy mobility debate suggests sometimes irreconcilable concepts and we still need concepts that address the spatial dimension of how urban housing policies travel between places. The article reﬂects on the extent to which selected concepts – policy knowledge, translation, and topologies – allow an explicit treatment of movement and materiality in a geographical understanding of housing policy mobilities. To cross-fertilize these concepts, the article revisits how key deﬁnitions relate to each other, and assesses the extent to which these concepts allow to understand the mobilization and localization of urban housing policies in particular contexts. Overall, the article offers a nuanced conceptualization of interurban movements and the spatial–material dimension of housing policies, and thereby enhances future empirical studies on urban housing policy.


Introduction
During a conference on housing in early 2019, Freiburg's deputy mayor for construction explicitly expressed the city's intention of receiving inspiration from elsewhere: "Do we have the right instruments, the right projects . . . I think . . . that we can simply be re-inspired and get a few examples of what can be done around housing" (Haag and Stadt Freiburg im Breisgau, 2019 1 ). Examples and lessons from other places were presented to Freiburg's municipal policymakers and practitioners by means of lectures and roundtables referring to models and best practices from Austria, Switzerland, the Netherlands, and within Germany. Germanspeaking presenters and participants came from various professions, including architects, planners, and researchers, as well as politicians, activists, and laypeople. This public conference is not just remarkable in regard of its setup as a forum for learning and knowledge circulation (Andersson and Cook, 2019;Cook and Ward, 2012). This conference also illustrates that housing policies' mobility takes place through 1 All translations from German are by the author.
the deliberate yet selective consultation of external ideas. Freiburg's housing conference thus offers a starting point for thinking about the increasing movement and mobilization of housing policies among cities in Europe.
In order to understand the mobility of urban housing policies, they are broadly defined as instruments, measures, and programmes which address the location, planning, and implementation of housing developments and the regulation of housing markets in cities. From a geographical perspective, housing policies have material implications and contribute to a real-estate fix -loosely following Harvey's (2001) "spatial fix" of capitalism -expressed in long-lasting, concrete forms in the built environment. This material dimension of housing policies has been particularly relevant for geographical understandings of housing as providing a place for dwelling through physical shelter, as a socio-spatial unit situating everyday practices in a particular neighbourhood, and as a protected private space (Wehrhahn, 2019:6). Such an understanding of housing does not necessarily coincide with a view of space "as a container within which the world proceeds" (Thrift, 2009:96). Rather, it is compatible with a relational view in which "space is seen as a co-product of those pro-ceedings" (Thrift, 2009:96). Building on Massey's (1994) relational view on place and home, housing is characterized by a dialectic of being global and local at the same time. Housing thus relates to a concrete place, yet the social relations that constitute it as a locality are not contained in the place itself but go beyond its conceived spatial limitations (Massey, 1994:162).
This dialectic of embeddedness and relationality presents the starting point for cross-fertilizing conceptualizations which understand urban housing policies as mobilized in between cities and as localized in particular contexts. Housing policies are embedded in a national and local context with a regulated room for manoeuvre. Often, urban governments in the same state adopt similar measures for influencing markets, reforming public programmes, and setting incentives for housing developments (see Rink and Egner, 2020, for a comparative overview of municipal housing policies in German cities). At the same time, housing policies respond to dynamic markets which involve transnational flows of capital, people, and information. Accordingly, the internationalization and financialization of the real-estate sector increasingly affect housing developments, which are no longer limited to local spheres of influence. As a consequence, local policymakers look to other places, intending to compete with and to learn from elsewhere. Hence, policy imitation and learning about innovative initiatives implemented in other places contribute to developing potent local responses to the current housing question 2 .
Urban housing policies present a particularly interesting example for analysing interurban policy circulation. The policy mobility approach has recently gained currency for studying housing policy movements (Soaita et al., 2020(Soaita et al., , 2021. Studies on the mobility of urban housing policies have focused on the movement of selected elements such as community land trusts (Thompson, 2018) or land value capture (Dembski et al., 2020). In their review of studies on the movement of housing policies, Soaita et al. (2021) however criticize that "the way the relevant concepts are deployed does not always fully reflect the sophistication of the literature from which they are drawn" (Soaita et al., 2021:17). So, in order to develop a nuanced understanding of urban housing policy movements, I draw from studies focusing on knowledge circulation in the built environment, addressing transnational building practices (Faulconbridge and Grubbauer, 2015) and the translation of ideas (Jacob and Lees, 2013). Faulconbridge (2015), notably, analyses the policy mobility of global models for the evaluation of sustainable buildings. He questions whether the adaptation of building models as a "sustainability fix" contributes to less local variety in building designs than deep green strategies such as local design adaptation (Faulconbridge, 2015:120). In a framework for understanding how mobility influences buildings and urban form, Guggenheim and Söderström (2009), furthermore, emphasize that ideas travel through human vectors, such as people, types, or media as human-and non-human materialities. In sum, housing policy mobility has received increasing scholarly attention, yet we still need to further develop concepts that address the spatial dimension of how urban housing policies travel between places and how they are translated to the built environment.
In the policy mobility debate, pertinent theoretical concepts such as knowledge, translation, and topologies are repeatedly mentioned, yet with sometimes "irreconcilable grammars of relationality" (Jacobs, 2012:412). These concepts are oftentimes not defined in a sufficiently differentiated way and the relationship between them is often unclear. Consequently, we need to be aware that "borrowed concepts smuggle with them ontological and epistemological assumptions that bear significant implications for geographers' understanding of space, the social, relationality, change, and power" (Martin and Secor, 2014:422). Thrift's (2009) suggestion of four different kinds of space offers an entry point for thinking geographically about policy mobility, which considers not only the material outcomes of housing policies, but also the relational connections through policy circulation, the imagined space which travels through presentations and brochures, and the place space, where knowledge is embedded in a particular context.
In this article, I therefore revisit concepts that particularly address how urban housing policymaking processes are relating to policy knowledge and techniques from elsewhere. What concepts offer an understanding of urban housing policies as mobilized in between cities and as localized in particular contexts? For understanding the relevance of interlocal relations, such concepts should address both the mobility of policy instruments and programmes, and localization processes through which housing policies are embedded in a particular context and translated into place-specific materializations. In particular, I discuss the notions of hybrid policy knowledge (Haughton et al., 2015), translation (Czarniawska and Joerges, 1996), and topological thinking (Robinson, 2013(Robinson, , 2015Prince, 2017). In order to cross-fertilize these concepts, I revisit key definitions of each of these concepts and how they relate to each other. In concrete terms, I assess the extent to which the selected concepts contribute to understanding the mobilization and localization of urban housing policies in particular contexts and how they address the spatial-material dimension of housing policies' mobility. The overall aim of this article is to develop a nuanced conceptualization of the interurban housing policy mobility, which serves as an example for developing a conceptual framework of the spatial-material dimension of policy mobility. I argue that the study of urban housing policies under the mobility perspective allows us to further develop key concepts for understanding the spatial dimension of policy movement. Overall, this article suggests explicit choices for exploring the mechanisms of policy mobility and thereby enhances future empirical studies on urban housing policy.
In the following section, I review the geographical debate on policy mobility, and discuss four particular characteristics that offer innovative lenses for studying mobile urban housing policies. The third section proceeds in three steps: Sect. 3.1 draws on a hybrid conceptualization of policy knowledge that goes beyond binary dichotomies of local/global and contextual/expert knowledge. Section 3.2 introduces the concept of translation as re-embedding of meaning and materialization. Section 3.3 explores topological thinking as a concept for understanding the relational entanglements involved in local policymaking. The cross-fertilization of these concepts thus proposes concrete approaches towards the mobility of urban housing policies suggested in Sect. 4, and is illustrated with examples from municipal housing policies in Germany, developing potential directions for future research.

A mobility perspective on urban housing policy
This section reviews academic debates in housing studies and on urban policy mobility, and brings them into a conversation, which is structured along four key aspects stemming from the policy mobility debate. Here, I discuss to what extent key characteristics of the policy mobility debate offer innovative lenses for a geographical understanding of the interurban circulation of housing policies, and thereby potentially open up new directions for housing studies.
First, policy mobility studies draw attention to political processes at the local-scale in order to overcome the methodological territorialism prevalent in earlier research on policy diffusion and transfer. Therefore, mobility scholars position themselves against political science's rational-institutionalist focus on policy movement between national states, and instead emphasize the relevance of interurban policy exchange (see among others Peck and Theodore, 2012:22-23). Accordingly, mobility scholars explore the circulation of urban policies by studying the inter-local movement of policy programmes, instruments, and concepts across time and space (see for overviews McCann, 2011;Temenos and Mc-Cann, 2013). Yet, within housing studies, the policy mobility approach has only recently gained currency (Soaita et al., 2020(Soaita et al., , 2021. Previously, comparative housing studies focused on national policies, along with a tendency towards methodological territorialism (Kemeny and Lowe, 1998; for an exception see Pickvance, 2001). Thereby, Lawson et al. (2010:9) ascertain that comparative methodologies for understanding policy transfer and cross-cultural learning in the 2000s remained rather underdeveloped, and comparative housing research instead focused on housing policies' transfer between national states (see also Oxley, 2001). In the meantime, several housing scholars developed a critical stance against limiting their research to national policies and questioned the transferability of housing policies from one context to another (see for an early account Allen et al., 1999). In their review, Lawson et al. (2010:9) point to new directions in comparative housing research which emphasize the limits of generalizations in cross-cultural comparison and instead identify an increased interest in social-constructivist concepts such as learning. Soaita et al. (2020), accordingly, identify policy mobility as an upcoming concept in housing studies since the mid-2000s for interpreting the movement of housing policies across time and space. Soaita et al. (2021:17), however, claim that the concepts drawn from the mobility debate for understanding housing policy movements are sometimes deployed superficially and need further development.
Second, policy mobility scholars take a particular interest in the processes of importing models, in policymaking as learning, and in the inter-local circulation, mutation, and adoption of policies McCann, 2012:1392). Thereby, mobility studies found new ways of addressing policies' local embeddedness and complex processes that lead to the grounding of mobile policies in one context (Cochrane and Ward, 2012:8). This focus on the local processes involved in policy mobility coincides with a shift in the mid-2000s in housing studies towards "micro-scale comparative studies, focusing on individual agents, their attitudes and beliefs, on micro-politics in different cities" (Matznetter, 2006:2). This shift towards context-sensitive, comparative analyses of urban housing policies has resulted in recent research agendas on the policy mobility of affordable housing (see Wetzstein, 2017Wetzstein, :3173, 2019. However, in-depth studies on the local processes of learning from elsewhere in urban housing policies are still scarce. Third, the policy mobilities debate offers a differentiated perspective on the geographies of policy circulation and the movement of urban concepts across time and space. Thereby, distinct ontological and epistemological choices influence the ways in which the mobilities of urban policies are analysed (Prince, 2012;Baker and Temenos, 2015;Jacobs, 2012:12). Among relational understandings of policy mobility, a more radical strand builds on assemblage approaches (Prince, 2017;McFarlane, 2011a). Such sociomaterial avenues towards radical relational thinking entail refusing the ontological differentiation "between materiality and meaning" (Davidson, 2021:26). Thereby, mobilities scholars have been particularly attracted to topological thinking (Robinson, 2013;Faulconbridge, 2013;Prince, 2017). Another more moderate relational approach on policy mobilities draws from concepts of local policymaking as learning and knowledge translation Mc-Cann, 2012:1393). Here, a relational understanding of space is complemented by social-constructivist conceptions of the interurban flow of ideas between sites. Baker et al. (2016) still see "scope for a deeper analysis of the ways in which people move ideas and the socio-spatial implications of ideas on the move" (Baker et al., 2016:460). Both rela-408 C. Fricke: Cross-fertilizing knowledge, translation, and topologies tional approaches can be fruitfully brought into conversation with social-constructivist approaches to comparative housing research (Haworth et al., 2004). However, ideational approaches and social-constructivist understandings of policy knowledge remain rather vague and need further specification.
Fourth, policy mobility approaches hold the potential to integrate both ideational and material perspectives on the travelling of ideas as suggested by planning scholars (see Raco and Savini, 2019 on different forms of knowledge in the planning process). Healey (2013), for example, suggests combining non-representational methods and interpretive concepts with studies on policy knowledge for understanding the transnational flow of planning ideas. The debate on the transnational flow of ideas and knowledge in urban policy and planning studies evolved -as pointed out by Jacobs (2012:413) -in parts complementarily, in parts parallel to the mobilities debate. Examples of travelling ideas include the international spread of New Urbanism as an urban design paradigm (Thompson-Fawcett, 2003) and the diffusion of the Barcelona model (Gonzáles, 2011). Moreover, in a practice-oriented, pragmatic view on planning and housing solutions, Lawrence (2021) calls for combining different forms of knowledge, learning, and lesson-drawing. These studies indicate that more concrete conceptualization of how travelling ideas matter for the built environment offers a refined understanding of the overall mobility of housing policies.
This overview on the junctures between the two academic debates underlines that the cross-fertilization of relational policy mobility debate with comparative and socialconstructivist approaches to housing policy studies holds the potential to develop a nuanced understanding of how mobility matters in the formation of urban housing policies.

Thinking policy mobility through knowledge, translation, and topologies
The following section reflects on the extent to which selected concepts -policy knowledge, translation, and topologiespotentially serve as connectors between housing studies and policy mobility research. Therefore, I revisit key definitions of each concept and explore how they relate to each other. First, I draw on a conceptualization of hybrid knowledge that goes beyond binary dichotomies of local/global and contextual/expert knowledge. Then, I revisit the concept of translation as re-embedding of meaning and materialization. Subsequently, I explore topological thinking for understanding the relational entanglements involved in local policymaking.

Towards hybrid understandings of policy knowledge
A key concern of policy mobility studies is what moves when a policy circulates from one context to another. Jacobs and Lees (2013) suggest that "when policy is seen to replicate itself . . . [what moves] is a far more disaggregated set of knowledges and techniques that are better thought of as pre-policy or sub-policy epistemes and practices" (Jabobs and Lees, 2013:1560). These policy components are regularly differentiated into policy knowledge on the one hand, and practices or techniques on the other. In doing so, policy mobility scholars reject a formalist conceptualization of knowledge as bounded and fixed, in order to go beyond an understanding of policies being moved as static, unchanged entities. Instead, policy mobility studies build on an understanding of knowledge as socially produced, multiple, and situated (McFarlane, 2011b:364). Thereby, the relational, social-constructivist strand of policy mobilities research lays a particular focus on "the embodied practices, representations, and expertise through which policy knowledge is developed, mobilized, and operationalized in different contexts" (McCann, 2011:120). The mobilities perspective "emphasizes that although knowledge might be understood to 'flow' around the world, it is only 'actionable' and productive when it is embedded or territorialized in specific social, spatial, and institutional contexts" (McCann, 2011:123). However, the way in which knowledge is treated in policy mobilities studies remains rather vague and needs further specification.
What concept of policy knowledge offers a better understanding of the mobility of urban housing policy? Corresponding to the plea to consider the situatedness of policy knowledge, I draw on a conceptualization of knowledge that aligns with a relational understanding of space (Thrift, 2009;Massey, 1991) beyond container thinking, and that conceives space as constituted through connections, images, and everyday practices. Relational thinking about place and locality as "constructed out of a particular constellation of social relations, meeting and weaving together at a particular locus" (Massey, 1991:28) requires us to rethink conceptualizations of knowledge and how it is embedded in particular contexts. Here, inspiration comes from studies on the relationship between knowledge, science, and local context which suggest overcoming binary, essentialist categories of knowledge (Clark and Murdoch, 1997;Lidskog, 2008;Haughton et al., 2015). These studies build on a progressive understanding of scientific knowledge as multifaceted, socially practised, and context-dependent. Previously, scientific knowledge's claim of universality permitted it to travel between different contexts (Clark and Murdoch, 1997:41), while recent views from the sociology of science underline "that all knowledge production and bodies of knowledge -irrespective of how far they have travelled -are situated; knowledge is always produced in, and part of the context of local cultural conditions" (Lidskog, 2008:79). Moreover, Haughton et al. (2015) suggest discarding the romanticism attached to naïve imaginations of traditional knowledge -acknowledging that "there is no such thing as pure local knowledge" (Haughton et al., 2015:385) -and instead focusing on the complex formation of contextual knowledge (Haughton et al., 2015:377). Thereby, hybrid knowledge stems from the mutual enhancement of scientific and local knowledge (Clark and Murdoch, 1997:56), from the interaction of different knowledge systems or cultures (Lawrence, 2021, see also Brown, 2010, leading to a more symmetrical relationship between different kinds of knowledge. From a geographical perspective, the situatedness of hybrid knowledge production raises questions related to generating, implementing, and utilizing knowledge, and to practices that allow knowledge to travel and to combine with other stocks of knowledge (Clark and Murdoch, 1997:42-43). To understand how geographical space matters for knowledge formation, Ibert (2007) suggests juxtaposing two ontologies, by drawing on a dichotomous understanding of the noun "knowledge" as an object and the verb "knowing" as a situated practice 3 . Geographical space matters for rationalistic, explicit knowledge through distance and proximity (Ibert, 2007:107), while knowing as a practice builds on the qualities of place or a concrete situation (Ibert, 2007:108). In line with this practice-based understanding of knowing, Haughton et al. (2015:377) suggest focusing on the communication and enactment of knowledge through interacting in concrete situations 4 . Such a spatialized understanding of hybrid policy knowledge enriches the study of urban housing policies in two ways. First, it gives a more detailed grasp of what travels when housing policies are mobilized. A geographical understanding of housing policy mobility focuses on the multiple forms of knowledge that are mobilized through interconnections -not only on the rationalistic, explicit forms of expert, technical, or scientific knowledgesbut also the situated learning practices that reveal more tacit ways of knowing. Second, the hybrid knowledge formation processes explore how knowledge is mobilized in a particular location or situation. Such practices of knowledge formation have received increasing attention from policy mobility scholars under the label of translation, which I will focus on in the next section. 3 Earlier anthropological policy studies, such as Yanow (2004:S12), differentiate between local and academic knowledge: local knowledge derives from a familiarity with a particular situation (know-how or practice), whereas technical, professional, and expert knowledge originates from academic training (know-that).
4 Examples for this second ontology of knowing as practice can also be found in research on co-production, defined as a process in which multiple forms of knowledge are included, contributing to an improved provision of public services, see Watson (2014). Thereby, the study of co-production of housing projects in which multiple forms of knowledge are combined, see Czischke (2018), could be further developed to deepen our understanding of translocal learning processes among alternative housing initiatives, see Hölzl (2022).

Translation as re-embedding of meaning and materialization
Policy mobility scholars frequently employ the concept of translation for describing the mutation of meaning when policies travel across space and time. Jacobs (2012) emphasizes that the concept of translation is key for understanding not only the movement itself "but also the multiplicity of add-ons that contribute, often in unpredictable and varying ways, to transportation, arrival, adoption and . . . non-arrival and nonadoption" (Jacobs, 2012:418). Regarding the spatial dimension, Jacobs and Lees (2013:1560) point out that the translation of knowledge and techniques takes place in situ. Similarly, Robinson (2015) states that the "arriving at" of policies is a local process and that policy ideas can be seen "as already profoundly local" (Robinson, 2015:832). Although ideas might have a history of circulating globally, "the relevant histories and processes by which they come to policymakers' attention might be entirely localized" (Robinson, 2015:832). How can we frame translation in conceptual terms to understand the local processes involved in the "arriving at" of urban housing policies? In the following, I further develop two complementary conceptualizations of translation: first, as a cognitive-linguistic process of re-embedding meaning between context; second, as the materialization of an idea into an object or something concrete in the physical sense of space.
Translation as re-embedding of meaning through language. In social sciences, translation is regularly understood as a process by which concepts are de-and recontextualized. This first understanding of translation draws from knowledge-based approaches in interpretive policy analysis and the Scandinavian institutionalist approach in organizational sociology. On the one hand, translation involves the mutation of meaning. Yanow (2004:S15-S16) reminds us that the process of translation is not a simple transfer of fixed, objectified knowledge without distortion of the original meaning. Instead, translation produces equivalence which occasionally requires changing a concept in order to make it meaningful in another context. This implies that we cannot assume equivalence between concepts or the commensurability of phenomena, problems, or policies, but their meaning depends on the particular context (Yanow, 2014:143). Moreover, Clarke et al. (2015) state that "[t]ranslation, then, is never neutral: some terms are translated, and some are not; some meanings are inscribed, while others are silenced" (Clarke et al., 2015:47). Here, Yanow (2004:S15) notes that a translator needs to be "bicultural" which requires familiarity with different contexts. Thus -building on a progressive understanding of hybrid knowledge developed in the previous section -a translator needs to speak multiple languages (Brown, 2010). This first understanding of translation as re-embedding meaning through language corresponds to the "travels of ideas"; a con-cept developed by Scandinavian institutionalists for explaining organizational change (Czarniawska and Joerges, 1996;Czarniawska and Sevón, 2005; see Schäfer, 2017 for a geographical adaptation of policy translation). Czarniawska and Joerges (1996) describe the translation of concepts between different moments and places -equivalent with the abovedescribed dis-and re-embedding of meaning -and from the abstract to the concrete. The latter implies that ideas are translated from objects to action, which corresponds to a second understanding of translation as materialization.
Translation as materialization. A second understanding of translation defines it as a process by which policy concepts and instruments convert immaterial flows of travelling ideas into material concreteness. Bok and Coe's (2017) conceptualize such a process in their study of the "corporate, crosssectorial dimension of how policies become mobile and territorialize" (Bok and Coe, 2017:55). They urge us to look at the "actual execution and grounding of knowledge in the built environment" (Bok and Coe, 2017:55) after the project was drafted and international consultation has taken place. Bok and Coe (2017) call this a process of "translation from planning to realization" (Bok and Coe, 2017:55), emphasizing the relevance of travelling agents and corporate actors 5 . How can we define such a process of materialization by which mobile housing policy knowledge and techniques are translated into the built environment? Here, the aforementioned differentiation of knowledge as an object and knowing as a practice adds an analytical value to understanding translation into the built environment: on the one hand, the translation process depends on knowledge codified in institutions and regulations (know-what). For example, Faulconbridge's (2013) study of green building design addresses such regulative, normative, and cultural institutions which situate and localize building design knowledge. Guggenheim and Söderström (2009), moreover, exemplify the translation process from the abstract to the concrete with building types, which are general classifications, linking the form of a building to social or functional classifications, and thereby conveying only essential features, "devoid of local references" (Guggenheim and Söderström, 2009:5). On the other hand, translation into the built environment is influenced by techniques and practices (know-how). For instance, such building types "have to be adapted to a new location because construction workers and architects use other building techniques and construction practices, because sites provide different materials" (Guggenheim and Söderström, 2009:6). Lovell (2007) puts a similar emphasis on materialities by drawing on a science and technology perspective on housing as a durable, capital-intensive infrastructure, which she illustrates based on demonstration projects translating new ideas into physical entities to promote and stabilize these ideas.
To understand the mobility of policy knowledge, the concept of translation offers two fruitful analytical dimensions. A first definition of translation understands it as the cognitive-linguistic practice of de-and re-contextualizing universal concepts into a particular context in time and space. This dimension of translation adds to the analysis of urban housing policy mobility by drawing the attention to the contextual embeddedness of meaning, challenging the unimpeded transferability of "best practices" or "models" between contexts. Moreover, this understanding of translation emphasizes the relevance of language for the mobilization of policy concepts and their transmission into different professional "jargons" such as legal instruments, financial subsidies, or visual building plans. The second definition of translation as materialization adds to the analysis of urban housing policies by focusing on their consequences in material space, through land allocation, buildings, and (infra-)structures. The concept of translation thus potentially connects cognitivelinguistic with spatial-material approaches offered by topological thinking described in the next section.

Topological thinking and sites of policy movement
Among the relational strand of policy mobilities research, topological thinking has recently received increasing attention (Robinson, 2013;Faulconbridge, 2013), and notably Prince (2017) suggests thinking "policy mobility beyond the local-global binary" (Prince, 2017:336) by adopting a topological conception of space (see also Allen, 2016:8;Allen and Cochrane, 2010). In the urban policy mobilities debate, topological thinking is often acclaimed to offer an understanding of the city beyond its territoriality, but as multiple policy arenas which are relationally and socio-politically constituted through de-territorialized conceptions of the city (Jacobs, 2012:415). Martin and Secor (2014:430) argue that its potential lies in understanding topologies not in contrast to topographies, but both as immanent and inseparable. So instead of privileging a relational focus on movement, they suggest framing topographical (Euclidian) space as one of a multiplicity of possible topological spaces (manifolds). Thereby, topological conceptions in policy mobility studies often build on actor network theory and assemblage approaches. Prince (2017), for instance, adopts Laws and Mol's topological thinking to understand "the active construction of networks and pipelines of policy knowledge across space, linking distant places and creating the conditions for certain kinds of policies to move between them" (Prince, 2017:335). This relates to Latour's understanding of translation as displacement, movement, and translocation (see Jacobs andLees, 2013:1562;Clarke et al., 2015:36), or as closure, as deciding what something means (Clarke et al., 2015:52).
To what extent do such ontologically more radical understandings of relational space offer a nuanced understanding of policy mobility? To understand the trans-local landscapes of policy mobility, Callon and Law (2004:3-4) suggest a conception of proximity and distance not as an opposition, but instead, they understand localization as being produced by multiple connections of intermediaries. Thereby, topology serves as heuristics for thinking about the relationships between elements, "as a way to think through and evoke a multiplicity of connections and relationships" (Hoffman and Thatcher, 2019:4). In such a topological understanding, "the local is an achievement in which a place is localized by other places and accepts 'localization' itself. But this means that no place is closed off, . . . each location is distributed in others" (Callon and Law, 2004:6). Accordingly, Prince (2016) suggests that "the city is not understood as a discrete entity, but as constituted through the relational connections that link them to other places, including other cities" (Prince, 2016:422). The concept of topologies frames mobile policies not as flowing from here to there, supposing separate locations, but as made of multiple connections, thinking here through elsewhere. This aligns with Robinson's (2013) suggestion to shift the focus of policy mobility studies to the process and sites of "arrival at" instead of the travelling itself. Topological thinking thus allows us to explore the "mixing and folding of here and elsewhere into distinctive local policies" (Robinson, 2013:20).
Considering a non-dichotomous understanding of proximity and distance, topological thinking analytically focuses on encounters and topographical sites of policy movement. Thereby, a "site is a place where something happens and actions unfold because it mobilizes distant actants that are both absent and present" (Callon and Law, 2004:6). In a topological conception of space, topographical policy sites are thus entry points to understand the manifold making of local policies. However, we still need to rethink our tactics to understand the processes that constitute topographical sites such as situations, meetings, or arenas which will be addressed in the next section.

Understanding the localization and materialization of urban housing policies
Rethinking key concepts for studying housing policies' mobility in the previous section entailed elaborating more detailed understandings of how policies move in between sites through translating housing political knowledge. The potential of connecting these concepts becomes visible when framed as analytical lenses for understanding concrete movements of housing policies. Instead of putting the elaborated concepts to an empirical test, the following paragraphs illustrate examples of doing future research drawn from policy movements in municipal housing policies in German cities. Notably, I discuss potential tactics for exploring the forma-tion of hybrid knowledge, translation processes, and topological landscapes of mobile urban housing policies.

Localization of hybrid knowledge and its translation
To track the topographical provenance of ideas poses a known challenge for studying movements and innovation in policy and planning. Healey (2013) notes that "the worlds within which an idea arrives and has effects may be far removed from the world which generated the momentum in which an idea was given initial shape and meaning" (Healey, 2013(Healey, :1517. In urban housing policies, ideas most obviously take shape through best practices and references to iconic models. As Freiburg's deputy mayor for construction explains: "Now when we get inspired, of course, we get the best cities in Europe. We'll get Vienna. Vienna is known for its housing policy, is currently one of the pioneers around the world. We get Munich, we get Amsterdam, we get Zurich where innovative new projects are being made" (Haag and Stadt Freiburg im Breisgau, 2019). Rhetorically, best practices in local housing policy are labelled by referring to the city as a whole. In fact, often only selected components of such policy packaging are travelling. An example from the municipal housing policy mix is Munich's directive for land allocation (Sozialgerechte Bodennutzung), which gives the municipality an instrument to share infrastructure and other costs with the private developer. This "Munich model" serves as a blueprint for other cities (Faller and Beyer, 2018) and is adapted to other local contexts (Pirzer and Wiegandt, 2020). Furthermore, other forms of knowledge in German housing policies are processed and generated by think tanks and consulting institutes, such as the difu (Deutsches Institut für Urbanistik) or the vhw (Bundesverband Wohnen und Stadtentwicklung). Both institutes act as influential knowledge brokers by translating local practices into national bodies of knowledge and vice versa based on surveys and workshops with local housing experts. To explore the localization of housing policies eventually implies studying the "loose threads" of learning between cities (Söderström and Geertman, 2013), which in the field of housing policies also takes place through professional associations and field trips.
Furthermore, a nuanced understanding of translation contributes to understanding how travelling ideas in the form of abstract knowledge are translated into local housing policies and building practices. Here, the concept of equivalence contributes to understanding commensurability through translation McCann, 2012:1393). For example, Freiburg's deputy mayor states: "We will take Berlin, because we can also think about what we can learn from cities like that. You cannot transfer this one-to-one, but of course, there are many things where we can also think about what we are doing in Freiburg. Maybe not in exactly the same way, but differently. But we find the Freiburg way with a lot of inspiration from outside" (Haag and Stadt Freiburg im Breisgau, 2019). Yet, to understand the localization of policy knowledge, we need to go beyond policy texts and ubiquitous paradigms, and focus on the knowledge formation processes itself instead (Prince, 2012:199). As outlined above, urban policies are not free-floating ideas and concepts, but need to be actively embraced, adapted, and emulated by local planners, civil servants, and policymakers. "Follow the translator" 6 means to study actors in the situation when they get inspired from elsewhere. This underlines that we need to change the analytical focus from the movement of people, ideas, and things to "how urban policymakers compose their ideas amidst the myriad of influences from elsewhere" (Robinson, 2015:831). Thereby, topological thinking offers an alternative view on the situations in which mobile policies are localized.

Researching topographical sites and materialization
Throughout the local policymaking process -preparing texts for concrete policy instruments; producing decisions in the local administration or elected council influenced by party politics, sectorial thinking, and other interests; and the consultation of the public during the making of plans for housing development -multiple forms of knowledge, at times from "elsewhere", contribute to the making of a concrete yet versatile set of practices assembled in the manifolds of urban housing policies. In previous research on policy mobility, to "follow the meeting" referred to conferences and other events for circulating policies (Wood, 2016:400). Similarly, Yanow (2014) suggests that "following policy components . . . lead analysts to trace the site of agenda setting, decision-making, and other locuses of power . . . without constraining the study within the borders of a specific physical setting. The policy itself is the site, not some geographically bounded entity" (Yanow, 2014:148). Topological thinking described above offers an alternative perspective on the relational landscapes of housing policy through which mobile ideas arrive at a particular site. To understand the multiple relationality of housing policies, we thus need to look at concrete situations where policy knowledge is translated into a particular context.
Following the topological sites of mobile housing policies implies going beyond the tracking from here to there, but encountering how situations such as workshops or conferences are made of connections to multiple "elsewheres". Here, the notion of "field event" (Ahlin and Li, 2019:4) goes beyond a topographical understanding of static moments, but proposes a relational understanding of events as being constantly cocreated and in movement, may it be virtually or physically in a particular location. Such spatio-temporal events allow us to witness translation practices in urban housing policies, if we understand the multiple connections bundled in this event, and if we recognize the different languages translated in the process. In addition, the embedding of policy knowledge in local contexts also takes place through desk research, closed meetings, and the engagement of local communities, activating situated knowledge through concrete practices such as participatory methods. In several larger German cities therefore, local housing policies include permanent alliances or round tables for incorporating alternative forms of knowledge from local associations and municipal housing companies (Böttcher, 2017). Furthermore, future research on urban housing policies' mobility should focus on the process of translation from an idea to an object which produces material artefacts. In terms of knowledge translation, the materialization through planning, constructing, and building involves practical knowledge and embodied practices. Potential examples for tracing the immediate materializations of local housing policies is the German tradition of international building exhibitions (Internationale Bauausstellung, IBA), which offer a playground for building experiments, incubators for social and technical innovations through housing models.

Conclusion
In this article, I reviewed selected concepts from the policy mobility debate and their potential for understanding the movement, localization, and materialization of urban housing policies. This conceptual article aimed to cross-fertilize the recent mobilities turn in housing studies with nuanced concepts from the policy mobility debate in urban geography and planning studies. The starting point was a relational approach to policy mobility and the identification of its key characteristics relevant for the analysis of urban housing policies. Furthermore, by defining key concepts from the mobilities debate -hybrid policy knowledge, translation, and topologies -and clarifying how they relate to each other, I developed a conceptual ground for understanding the interurban dimension of urban housing policies.
First, the article underlines that a geographical study of housing policy mobility needs to focus on multiple forms of situated knowledge mobilized through interconnections -the rationalistic, explicit forms of expert, technical, or scientific knowledges, and the situated practices that reveal tacit ways of knowing in a particular location or situation. In particular, these nuanced forms of knowledge and their hybrid formation allow us to understand how knowledge on urban housing policies moves across places and sites. Thereby, the differentiation of knowledge as a noun and as a practice entails both the relational dimension of policy movement and the process of embedding knowledge in a local context. Second, despite their common origins in assemblage thinking and actor network theory, the two reviewed understandings of translation evolved differently, in particular regarding their underlying conceptualizations of space. Considering the different understandings of translation, I argue that the potential of transla-tion as an analytical concept lies in its bridging of different grammars of relationality: translation can be understood not only as a metaphor for the transfer of policies between local context, but also as the process of implementing abstract ideas into the concrete. Topological thinking, thirdly, offers a new perspective on the local and trans-local dimension of housing policies as assembled through their relations in topographical events or encounters. The focus on local political processes and place-specific materializations moreover allows a deeper understanding of the "arriving at" and localization of housing policies. Finally, these conceptual choices hold implications for empirical approaches. To understand the localization and materialization of mobile housing policies, potential future research should engage with in-depth enquiries on how housing policies arrive at local contexts and how they are translated into the built environment. This focus on local processes potentially generates new insights on how urban housing policies change due to the interplay of global and local connections, and as a process of translation of policy knowledge from elsewhere.
Overall, the theoretical cross-fertilizing uncovers common conceptual grounds in the policy mobilities debate in urban geography and housing studies. Thereby, this article underlines how more nuanced conceptualizations of policy knowledge, translation, and topological thinking offer entry points for a geographical understanding of mobile urban housing policies. Combining these concepts allows analysing crucial elements of the process through with policies are mobilized in between cities and localized in particular contexts. Thereby, various questions arise for future research on housing policy movements. For instance, we still know little about the formation of hybrid knowledge in housing policies: how do urban policymakers select best practices to learn from? To what extent do cities promote their own housing policies as best practise? Such questions could contribute to exploring the genesis of iconic models in housing policy. Moreover, in which situations, sites, and events are housing policies mobilized? How are housing policies from elsewhere embedded in local urban contexts?
With regard to their meanings elaborated above, the concepts offer an innovative geographical perspective on policy movement that considers the dialectic of embeddedness and relationality of housing in particular. Thereby, urban housing policies served as an exemplary policy field, which entails particular challenges, but also opportunities for studying the social dimension -through ideational and cognitive approaches -as well as the spatial dimension -material and topological understandings -of policy mobilities.
Data availability. No data sets were used in this article.
Competing interests. The author has declared that there are no competing interests.

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