Quantum Curves in Chern-Simons Theory

Geometry Topology Seminar
Wednesday, January 19, 2011 - 15:05
1 hour (actually 50 minutes)
Skiles 006
IAS, Princeton
I will discuss a new general framework for cutting and gluing manifolds in topological quantum field theory (TQFT). Applying this method to Chern-Simons theory with gauge group SL(2,C) on a knot complement M leads to a systematic quantization of the SL(2,C) character variety of M. In particular, the classical A-polynomial of M becomes an operator "A-hat", the same operator that appears in the recursion relations of Garoufalidis et al. for colored Jones polynomials.