The Kauffman Skein Module at 1st Order. (12th December 2019)

• Record Type: Journal Article
• Authors: Marché, Julien
• Is Part Of: International mathematics research notices. Volume 2021:Number 22(2021)
• Page Start: 17413
• Page End: 17432
• Publication Date: 2019-12-12
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnz289
• Languages: English
• ISSNs: 1073-7928

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.