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2019 Generalized Kuperberg invariants of $3$–manifolds
Rinat Kashaev, Alexis Virelizier
Algebr. Geom. Topol. 19(5): 2575-2624 (2019). 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.

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Rinat Kashaev. Alexis Virelizier. "Generalized Kuperberg invariants of $3$–manifolds." Algebr. Geom. Topol. 19 (5) 2575 - 2624, 2019. https://doi.org/10.2140/agt.2019.19.2575

Information

Received: 18 June 2018; Revised: 5 November 2018; Accepted: 17 November 2018; Published: 2019
First available in Project Euclid: 26 October 2019

zbMATH: 07142613
MathSciNet: MR4023323
Digital Object Identifier: 10.2140/agt.2019.19.2575

Subjects:
Primary: 57M27
Secondary: 16T05

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.19 • No. 5 • 2019
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