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Article Dans Une Revue Algebr.Geom.Topol. Année : 2022

Twisting Kuperberg invariants via Fox calculus and Reidemeister torsion

Résumé

We study Kuperberg invariants for sutured manifolds in the case of a semidirect product of an involutory Hopf superalgebra $H$ with its automorphism group $\text{Aut}(H)$. These are topological invariants of balanced sutured 3-manifolds endowed with a homomorphism of the fundamental group into $\text{Aut}(H)$ and possibly with a $\text{Spin}^c$ structure and a homology orientation. We show that these invariants are computed via a form of Fox calculus and that, if $H$ is $\mathbb{N}$-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.

Dates et versions

hal-02423723 , version 1 (25-12-2019)

Identifiants

Citer

Daniel López Neumann. Twisting Kuperberg invariants via Fox calculus and Reidemeister torsion. Algebr.Geom.Topol., 2022, 22 (5), pp.2419-2466. ⟨10.2140/agt.2022.22.2419⟩. ⟨hal-02423723⟩
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