ABSTRACT
Topology, chaos theory, and psychoanalytic semiotics are only beginning to be integrated. Much promise exists for these novel conceptual tools for critical examination in the social sciences. Integrating critically informed psychoanalytic semiotics, topology and chaos theory offer much potential for developing new insights in doing postmodern criminology. This chapter outlines two of the key topological constructs used by Jacques Lacan and indicates the relevance for doing postmodern criminology. It deals with the question of how narratives and stories are constructed: be they by citizens, witnesses, police; or in reports and testimony, trial proceedings, court opinions, newspaper accounts, and scholarly research. The chapter explains the relevance for doing critical criminology in the application of the Mobius band, cross-cap, and borromean knots. It provides a phase portrait of two coupled phenomena—desire and demand—and how demand always misses its mark, never precisely reflecting desire.
