木村直記

Title:
A generalization of the Dijkgraaf-Witten invariant for cusped 3-manifolds

Abstract:
The Dijkgraaf-Witten invariant is a topological invariant for compact oriented 3-manifolds in terms of a finite group and its 3-cocycle.  The invariant is a state sum invariant constructed by using a triangulation, likewise the Turaev-Viro invariant.  In this talk, we consider a generalization of the Dijkgraaf-Witten invariant for cusped 3-manifolds.  We show that the generalized Dijkgraaf-Witten invariants distinguish some pairs of orientable cusped hyperbolic 3-manifolds with the same hyperbolic volumes and with the same Turaev-Viro invariants. We also give an example of a pair of cusped hyperbolic 3-manifolds with the same hyperbolic volumes and with the same homology groups, meanwhile with distinct generalized Dijkgraaf-Witten invariants.