The Kauffman Skein Module at 1st Order. (12th December 2019) - Marché, Julien
Abstract: For a three-manifold M with boundary, we study the Kauffman module with indeterminate equal to -1+ε where ε ^2=0 . We conjecture an explicit relation between this module and the Reidemeister torsion of M, which we prove in particular cases. As a maybe-useful tool, we then introduce a notion of twisted self-linking and prove that it satisfies the Kauffman relations at 1st order. These questions come from considerations on asymptotics of quantum invariants.