ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: 57Q15, 57Q45 Carter, J. Scott, University of South Alabama; Saito, Masahico, University of South Florida; Kauffman, Louis, University of Illinois, Chicago The Diagrammatics of Hopf Categories and Invariants of 4dimensional Manifolds The axioms for a Hopf Category, as developed by Crane and Frankel, can be used to define a state-sum invariant of 4-dimensional manifolds provided certain finiteness conditions hold. In this talk, we discuss the Hopf category associated to the Drinfeld double of a finite group. A coloring of the (1, 3)-flags allows one to weight tetrahedra, triangles, and dual tetrahedra by cocycles to define such an invariant. We show a direct correspondence among the cocycle conditions, the coherence cubes, and the moves to triangulations of 4-manifolds. We relate other cocycles to the construction of invariants of knotted surfaces.