The Kauffman Skein Module at 1st Order

Abstract

Abstract For a three-manifold $M$ with boundary, we study the Kauffman module with indeterminate equal to $-1+\epsilon $ where $\epsilon ^2=0$. 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.