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Generalized Kuperberg
invariants of $3$–manifolds
Rinat Kashaev and Alexis Virelizier |
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Algebraic & Geometric Topology 19 (2019) 2575–2624
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Abstract |
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In the 1990s, based on presentations of –manifolds by Heegaard diagrams, Kuperberg associated a scalar invariant of –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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Keywords
invariants of $3$–manifolds, Hopf algebras
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Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 16T05
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References |
Publication
Received: 18 June 2018
Revised: 5 November 2018
Accepted: 17 November 2018
Published: 20 October 2019
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Authors |
| Rinat Kashaev | |
| Section de Mathématiques Université de Genève Genève Switzerland |
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| Alexis Virelizier | |
| Départment de Mathématiques Université de Lille Villeneuve France |
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