The Kauffman skein module at first order

Julien Marché

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arXiv · 1510.09111

The Kauffman skein module at first order

Julien Marché

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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.

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Julien Marché. 2015-10-30. The Kauffman skein module at first order. https://arxiv.org/abs/1510.09111

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