It is commonplace and even intuitive to think of character in terms of the analogy of the body: a personal interiority marked off by clear boundaries from the impersonal and very different world outside it, like an irregular sphere. The complexities of the so-called "initial style" of Ulysses, however, point to other relationships. That seemingly realistic braid of naturalistic dialogue, minimal narration, and the private floridities of interior monologue has other effects altogether once we consider the extraordinary fluidity and inventiveness of Joycean free indirect discourse. This essay uses a number of topologies other than the sphere to describe some of these effects and to examine some of their implications. In doing so, it draws on Jacques Lacan's turn to these topologies in the early 1960s.