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Kuperberg invariants for balanced sutured 3-manifolds

Part of: Low-dimensional topology Hopf algebras, quantum groups and related topics

Published online by Cambridge University Press:  20 August 2020

Daniel López Neumann
Daniel López Neumann*
Affiliation:
Institut de Mathématiques de Jussieu—Paris Rive Gauche, Université de Paris, Paris, France
*
e-mail: daniel.lopez@imj-prg.fr
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Abstract

We construct quantum invariants of balanced sutured 3-manifolds with a ${\text {Spin}^c}$ structure out of an involutive (possibly nonunimodular) Hopf superalgebra H. If H is the Borel subalgebra of ${U_q(\mathfrak {gl}(1|1))}$ , we show that our invariant is computed via Fox calculus, and it is a normalization of Reidemeister torsion. The invariant is defined via a modification of a construction of Kuperberg, where we use the ${\text {Spin}^c}$ structure to take care of the nonunimodularity of H or $H^{*}$ .

Keywords

Kuperberg invariantsHopf algebrassutured manifoldsReidemeister torsion

MSC classification

Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 16T05: Hopf algebras and their applications
Type
Article
Information
Canadian Journal of Mathematics , Volume 73 , Issue 6 , December 2021 , pp. 1698 - 1742
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Copyright
© Canadian Mathematical Society 2020

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Footnotes

This project has received funding from the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement No. 665850.

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