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2022 Twisting Kuperberg invariants via Fox calculus and Reidemeister torsion
Daniel López Neumann
Algebr. Geom. Topol. 22(5): 2419-2466 (2022). DOI: 10.2140/agt.2022.22.2419

Abstract

We study Kuperberg invariants for sutured manifolds in the case of a semidirect product of an involutory Hopf superalgebra H with its automorphism group Aut(H). These are topological invariants of balanced sutured 3–manifolds endowed with a homomorphism of the fundamental group into Aut(H), and possibly with a Spinc structure and a homology orientation. We show that these invariants are computed via a form of Fox calculus and that, if H is –graded, they can be extended in a canonical way to polynomial invariants. When H is an exterior algebra, we show that this invariant specializes to a refinement of the twisted relative Reidemeister torsion of sutured 3–manifolds. We also give an explanation of our Fox calculus formulas in terms of a particular Hopf group-algebra.

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Daniel López Neumann. "Twisting Kuperberg invariants via Fox calculus and Reidemeister torsion." Algebr. Geom. Topol. 22 (5) 2419 - 2466, 2022. https://doi.org/10.2140/agt.2022.22.2419

Information

Received: 4 November 2020; Revised: 14 April 2021; Accepted: 3 June 2021; Published: 2022
First available in Project Euclid: 10 November 2022

Digital Object Identifier: 10.2140/agt.2022.22.2419

Subjects:
Primary: 57K16 , 57K31
Secondary: 16T05

Keywords: quantum invariants , Reidemeister torsion , sutured manifolds

Rights: Copyright © 2022 Mathematical Sciences Publishers

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Vol.22 • No. 5 • 2022
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