The Turaev-Viro Invariant away from roots of unity.
by
Charles Frohman
The University of Iowa
Coauthors: Joanna Kania-Bartoszynska

We will work with a deformation parameter which is a complex number t with |t|<1. It is chosen to coincide with A in the standard development of the Kauffman bracket. The asymptotics of the quantum 6j symbols are a good deal simpler when |t|<1, as opposed to |t|=1. This allows us to analyze the convergence properties of the state sum formulation of the Turaev-Viro invariant away from the unit circle. The outline of the talk will be as follows. 1. Asymptotics of the 6j-symbols. 2. Extension of Turaev's shadow world away from roots of unity. 3. Representation theoretic expalanation as t approaches -1. 4. A ``TQFT'' for the Turaev-Viro invariant away from roots of unity. The parenthesis are because you cannot have a TQFT where the vector spaces of observables are infinite dimensional, you can however see a three-manifold as defining a linear functional on the Kauffman bracket skein module of its boundary.

Date received: March 10, 2002

Copyright © 2002 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 # caiy-02.