Abstract

The Kauffman bracket skein module of an oriented 3-manifold M is a vector space (depending on a parameter q) which is generated by framed links in M modulo certain skein relations. The goal for the talk is the explain our recent proof (joint with David Jordan and Pavel Safronov) that the skein module of a closed 3 manifold is finite dimensional for generic q, confirming a conjecture of Witten. The proof involves interpreting skein modules as deformation quantization of SL(2,C)-character varieties, and uses a result on holonomic modules due to Kashiwara and Schapira. Time permitting, I will explain the connection with Abouzaid—Manolescu’s sheaf theoretic model for Floer cohomology.