The Kauffman skein module at first order

Abstract

For a 3-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 first order. These questions come from considerations on asymptotics of quantum invariants.

14 pages, 4 figures

References in corpus (3)

• Asymptotics of the colored Jones function of a knot
• SL(2,C) Chern-Simons theory and the asymptotic behavior of the colored Jones polynomial
• Torus knot state asymptotics