Generalized Kashaev and Turaev-Viro 3-manifold invariants

Geometry Topology Seminar
Monday, April 11, 2011 - 2:00pm
1 hour (actually 50 minutes)
Skiles 006
Utah State University
I will consider two constructions which lead to information about the topology of a 3-manifold from one of its triangulation.  The first construction is a modification of the Turaev-Viro invariant based on re-normalized 6j-symbols.  These re-normalized 6j-symbols satisfy tetrahedral symmetries.  The second construction is a generalization of Kashaev's invariant defined in his foundational paper where he first stated the volume conjecture.  This generalization is based on symmetrizing 6j-symbols using *charges* developed by W. Neumann, S. Baseilhac, and R. Benedetti.  In this talk, I will focus on the example of nilpotent representations of quantized sl(2) at a root of unity.  In this example, the two constructions are equal and give rise to a kind of Homotopy Quantum Field Theory.  This is joint work with R. Kashaev, B. Patureau and V. Turaev.