The Kauffman skein module at first order

2015/10/30 by Julien Marché, Marché, Julien
Mathematics · #57M27 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M27

paper · pdf · doi:10.48550/arxiv.1510.09111

14 pages, 4 figures

arxiv created 2019/09/27 · arxiv updated 2019/09/30

Abstract

For a 3-manifold M with boundary, we study the Kauffman module with indeterminate equal to -1+ε where ε²=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.

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