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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
Kashaev, Rinat 1 ; Virelizier, Alexis 2
@article{10_2140_agt_2019_19_2575,
author = {Kashaev, Rinat and Virelizier, Alexis},
title = {Generalized {Kuperberg} invariants of 3{\textendash}manifolds},
journal = {Algebraic and Geometric Topology},
pages = {2575--2624},
publisher = {mathdoc},
volume = {19},
number = {5},
year = {2019},
doi = {10.2140/agt.2019.19.2575},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2019.19.2575/}
}
TY - JOUR AU - Kashaev, Rinat AU - Virelizier, Alexis TI - Generalized Kuperberg invariants of 3–manifolds JO - Algebraic and Geometric Topology PY - 2019 SP - 2575 EP - 2624 VL - 19 IS - 5 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2019.19.2575/ DO - 10.2140/agt.2019.19.2575 ID - 10_2140_agt_2019_19_2575 ER -
%0 Journal Article %A Kashaev, Rinat %A Virelizier, Alexis %T Generalized Kuperberg invariants of 3–manifolds %J Algebraic and Geometric Topology %D 2019 %P 2575-2624 %V 19 %N 5 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2019.19.2575/ %R 10.2140/agt.2019.19.2575 %F 10_2140_agt_2019_19_2575
Kashaev, Rinat; Virelizier, Alexis. Generalized Kuperberg invariants of 3–manifolds. Algebraic and Geometric Topology, Tome 19 (2019) no. 5, pp. 2575-2624. doi: 10.2140/agt.2019.19.2575
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