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2020 Nonsemisimple quantum invariants and TQFTs from small and unrolled quantum groups
Marco De Renzi, Nathan Geer, Bertrand Patureau-Mirand
Algebr. Geom. Topol. 20(7): 3377-3422 (2020). DOI: 10.2140/agt.2020.20.3377

Abstract

We show that unrolled quantum groups at odd roots of unity give rise to relative modular categories. These are the main building blocks for the construction of (1+1+1)–TQFTs extending CGP invariants, which are nonsemisimple quantum invariants of closed 3–manifolds decorated with ribbon graphs and cohomology classes. When we consider the zero cohomology class, these quantum invariants are shown to coincide with the renormalized Hennings invariants coming from the corresponding small quantum groups.

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Marco De Renzi. Nathan Geer. Bertrand Patureau-Mirand. "Nonsemisimple quantum invariants and TQFTs from small and unrolled quantum groups." Algebr. Geom. Topol. 20 (7) 3377 - 3422, 2020. https://doi.org/10.2140/agt.2020.20.3377

Information

Received: 1 January 2019; Revised: 11 December 2019; Accepted: 3 January 2020; Published: 2020
First available in Project Euclid: 5 January 2021

MathSciNet: MR4194285
Digital Object Identifier: 10.2140/agt.2020.20.3377

Subjects:
Primary: 57M27, 81R50

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.20 • No. 7 • 2020
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