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.