Generalized Kuperberg invariants of 3–manifolds

Kashaev, Rinat; Virelizier, Alexis

doi:10.2140/agt.2019.19.2575

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Generalized Kuperberg invariants of $3$–manifolds

Rinat Kashaev and Alexis Virelizier

Algebraic & Geometric Topology 19 (2019) 2575–2624

DOI: 10.2140/agt.2019.19.2575

Abstract

In the 1990s, based on presentations of $3$ –manifolds by Heegaard diagrams, Kuperberg associated a scalar invariant of $3$ –manifolds to each finite-dimensional involutory Hopf algebra over a field. We generalize this construction to the case of involutory Hopf algebras in arbitrary symmetric monoidal categories admitting certain pairs of morphisms called good pairs. We construct examples of such good pairs for involutory Hopf algebras whose distinguished grouplike elements are central. The generalized construction is illustrated by an example of an involutory super-Hopf algebra.

Keywords

invariants of $3$–manifolds, Hopf algebras

Mathematical Subject Classification 2010

Primary: 57M27

Secondary: 16T05

References

Publication

Received: 18 June 2018

Revised: 5 November 2018

Accepted: 17 November 2018

Published: 20 October 2019

Authors

Rinat Kashaev
Section de Mathématiques Université de Genève Genève Switzerland

Alexis Virelizier
Départment de Mathématiques Université de Lille Villeneuve France

Volume 19, issue 5 (2019)