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abstract: 'In the 90s, 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.'
address:
- 'Section de mathématiques, Université de Genève, 2-4 rue du Lièvre, 1211 Genève 4, Suisse\'
- 'Département de mathématiques, Université de Lille, Cité Scientifique, 59655 Villeneuve d’Ascq, France\'
author:
- Rinat Kashaev
- Alexis Virelizier
title: 'Generalized Kuperberg invariants of 3-manifolds'
---

Introduction
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In the 90s, G. Kuperberg in [@Ku1] defined a scalar invariant of closed oriented 3-manifolds by using arbitrary finite-dimensional involutory Hopf algebra over a field. The combinatorics of Kuperberg’s construction comes from the presentation of 3-manifolds by Heegaard diagrams and the invariant is calculated by using the tensor products of the structural morphisms of the Hopf algebra contracted with appropriate tensor products of (two-sided) integrals and cointegrals of the Hopf 