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As objects of anthropological inquiry, a body, a house, and a territory each pose a similar set of questions in relation to notions of interiority/exteriority; identity/alterity; limit or boundary; and containment. The body, the house, and the territory “locate” these questions on different scales. I will address them through three case studies that overall take up Henri Lefebvre’s challenge to examine how spaces “interpenetrate one another.”[1] My purpose is to explore the relevance of using topology as a method of analysis in these three cases. At this stage in this exploration, for me, topology remains a tool that can help reformulate some anthropological questions.[2] Let me introduce this first text with some general considerations about the common conceptual framework that equally apply to the next two.In anthropology,Edmund Leach[3]famously drew a parallel between kinship patterns that are reproduced insimilar ways across different societies and topology as a geometry of elasticrubber sheeting. Such an analogy served him well in showing that the size, shapeor distance between “things” (groups) is less significant than what holds themtogether: as in an elastic topological space, what matters is the way “things”are connected and the continuity of the relations thus established. Topology isincreasingly making an appearance across the social sciences and thehumanities. Various attempts at making use of topology beyond the field ofmathematics have turned to other topological figures such as the Klein bottle,the Möbius strip, a crushed handkerchief, or a fold.[4]A common characteristic of these attempts is the understanding that topologydeals with the qualitative properties of shapes (geometrical structures) andstudies their structural invariance under deformation. Mathematical objects are certainly quite distinctfrom those in social sciences, but a topological lens can help reveal how social phenomenaexhibit a similar dynamic of continuity or constancy of relations in spite ofchange through space and time.Moving away fromdominant conceptualizations of bounded entities and other totalities and focusinginstead on relations and forms of multiplicity and singularity, involves generating thepossibility for new social geometries where it is relations that bind andexchanges that group. Such an approach is in keeping with anthropology’sattention to rules of connection or disconnection, and theprocesses through which those relations are reproduced, and yet continuallychanged or transformed. Atopological imagination enables us to articulate various continuities andlimits that are constitutive of the nesting of spaces: in other words, the emergentforms of the spatiality of life.*&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160; *&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160; *The first case study dealswith conceptualization of the (woman’s) body in relation to tattooing. It takesus to Southwest China, where Yunnan, Tibet, and Myanmar meet. There, among theDrung people, women’s facial tattoos are still a cultural icon today. However,women abandoned the practice of tattooing two generations ago. For Drung women,the facial tattoo (bāktūq) used to be a keyelement in a socialization process. Based on what I learned from elderly tattooed women, Iwish to highlight how the tattooing process reveals the woman’sbody as a cosmological assemblage in which diverse forces condense into an interplaybetween the outside and the inside. The tattoo technique, aspracticed by Drung women, contributed to their transition to womanhood by meansof productive exchanges and influences. Tattoos were the mark of time (bothphysiological and social) and the mark of destiny, preparing women for whenthey become fertile. While the tattooing of Drung women wasnot an initiation rite in a conventional sense, it nevertheless constituted a prescribed and mandatory event for all girls prior to marriage,which contributed to their transformation.Even before the nubile age, aform of reciprocal fashioning took place between women (or girls)via tattooing games (generally on their arms or legs); acts also effective in transmitting femininity. These trial runs on the arms or legs were a way ofexperimenting with the bodily experiences involved in the tattooing process(pain, bleeding, swelling, warmth…). The notion of play (agàl), often used to refer to these games, emphasizes a processrather than an event, as play is a modality of the transformation it triggers. Therefore,before having their face tattooed, girls had access—in a playful way—to a sort of“social puberty,” which served as a gradualtransition. Following on from the playful trial runs performed by girls ontheir bodies, the facial tattoo is not in itself the acknowledgement of the menarchebut thecontinuation of a transformative process. In other words, in its cumulativeactions, tattooing as a process iscomparable to an initiation that prepared a woman for marriage and her role asmother.[5]Now, as a process oftransformation through which a particular fashioning and transmission occur,tattooing involves more specifically an interplay between interiority andexteriority that is full of potentiality and danger.Both—potentiality anddanger—are explicit and particularly salient when the facial tattoo isperformed. The power of the exclusively female tattoo artists—of the countless pricksand what they contribute to bringing about—is to reveal a power that isspecific to women.In this process that “reveals” the fertile potential of a woman, there is also thepotential danger for the tattooist of no longer seeing properly, of having her “eyesaffected” (nēq-ma), that is, of her own fertility being reduced.Thetattooed face is coded by a multidimensional corporeal code in which the faceis now a surface totally covered in prick holes (eyes). The woman who receivesthe tattoo manifests a potentiality, a power that threatens the other woman,the tattoo artist, who has enabled this transformation. To be more precise, itis like giving birth. The woman who attends childbirth runs the same risk: ofhaving her eyes and vision affected. In both cases, therefore, the women whohelp with tattooing or giving birth are in contact with what is a manifestationof a potentially dangerous feminine power—often symbolized by the presence of bloodand expressed through an analogy with the eye. They must be given compensation inkind (various typically feminine goods) in order to “wash [their] eyes.”The gradual construction offeminine power revealed by the tattoo on Drung women’s faces seems to beinseparable from the transmission that takes place between women. It is a specificallyfeminine transmission and, as such, establishes a form of relatedness (continuity) thatassociates women with a generative capacity. The tattoos are vectors ofwomanhood whose effectiveness depends just as much on the cumulative aspect ofpreparatory play, the multiple pricks of the spine, as on what circulatesbetween and through women: a stimulating flow of female generative propertiesthat allow each individual to ensure her destiny whose collective goal is toperpetuate society. Eachtattoo, seen through this relational lens, is a unique actualization but also asign of belonging and relatedness, of what used to bind women together.This circulation and appropriation of a feminine generative power leads us toconsider the body as the site of an intersubjectiveactualization and participation. As Terence Turner[6]emphasized, the “social skin” is an interface more than a surface. The outside environmentdoes not stop at the surface of the body, and individuals are not isolated withintheir own body but interlinked deep in their flesh by social relationships. Asa result, a woman’s facial tattoo is aninside that presents the highest relativity—a fold of the outside, theexteriorization of the interior and simultaneously the interiorization of theexterior. As Alfred Gell put it: the tattoo reveals “an inside which comes fromthe outside, which has been applied externally prior to being absorbed into theinterior.”[7] In our case, the face is the interface thatmediates the process of the individuation of the woman through the permanenceof the tattoo that is necessary to stabilizethe generative force of life as socially reproductive. In sum, tattooing amongDrung women relied on a strictly female lineality, a flow of similarity, whichimplies concomitantly an incorporation and an exteriorization, a process thatin turn instantiated a differentiation in each woman by unveiling hergenerative value.[1] Henri Lefebvre. 1991. The Production of Space. Oxford: Blackwell, p. 86.[2] I have greatly benefited fromdiscussions with Khashayar Beigi, Kamala Russell, and William Stafford at UCBerkeley where we started a Topology Working Group.[3] See the introductory chapter in Edmund R. Leach, 1961. Rethinking Anthropology. New York: The AthlonePress.[4] Thevarious engagements with and discussions of topology in the social sciences aretoo numerous to be referenced here. This is a work in progress and a literaturereview goes beyond the scope and limits of this blog post.[5] For a more detailed description, see Stéphane Gros, 2017. “Quand les femmes font corps. Le tatouage facial féminin chez les Drung du Yunnan.” In Le Battement de la vie. Le corps naturel et ses représentations en Chine, edited by Brigitte Baptandier. Nanterre: Société d’ethnologie, pp.163-187.[6] Terence Terence. 2012 [1980]. “The social skin.” Hau: Journal of Ethnographic Theory 2 (2): 486-504.[7]Alfred Gell. 1993. Wrapping in Images: Tattooing in Polynesia. London:Clarendon Press, p. 38.