Mapping Class Group Representations via TQFT's
by
Thomas Kerler
The Ohio State Univeristy

We discuss two types of representations of the mapping class groups that arise from the quantum constructions of TQFT's. One is obatined from the TQFT-generalization of the Hennings invariant, starting from an 8-dimensional Hopf algebra. It is shown to reproduce the homological intersection TQFT and MCG reps of Frohman and Nicas. Using the Reshtikhin Turaev procedure at a 5-th root of unity and the results of Kirby, Melvin and Murakami we obtain MCG reps that give rise to interesting formulas for the Casson invariant.

Date received: May 12, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeu-09.