This chapter considers the topological ordering of urban space enabled by mobile computing devices, using London as a field site and example. Building on theory developed by Scott Lash, Rob Shields and others, I first distinguish between virtual and topological figurations of the city. I then consider the various implications of topological spatiality for urban politics, before moving on to an attempt to empirically develop a typology of mobile applications centred on London, each offering different opportunities for urban encounter and (...) representation. The central argument advanced in this chapter is that mobile-enabled topologies are important and increasingly routine social imaginaries with the potential to radically disrupt other kinds of socio-spatial order. (shrink)