On mapping class group representations coming from Integral TQFT
by
Gregor Masbaum
Institut de Mathematiques de Jussieu

The Witten-Reshetikhin-Turaev TQFT-invariants of 3-manifolds give rise to finite dimensional representations of mapping class groups. In this talk, I want to explain some things one can learn about these representations by using the integral theory constructed in joint work with Patrick Gilmer. First, I will describe how to approximate the representation at a fixed prime p by representations into finite groups, and I will give explicit formulas for this approximation in the case of a torus with one boundary component. Second, I will show how to take an Ohtsuki-style limit of the representations as p goes to infinity. This is expected to be related to Witten's asymptotic expansion conjecture.

Date received: May 30, 2009