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Nonsemisimple quantum
invariants and TQFTs from small and unrolled quantum
groups
Marco De Renzi, Nathan Geer and Bertrand Patureau-Mirand |
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Algebraic & Geometric Topology 20 (2020) 3377–3422
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Abstract |
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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 –TQFTs extending CGP invariants, which are nonsemisimple quantum invariants of closed –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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Keywords
nonsemisimple quantum invariants, nonsemisimple TQFTs,
small quantum groups, unrolled quantum groups
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Mathematical Subject Classification 2010
Primary: 57M27, 81R50
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References |
Publication
Received: 1 January 2019
Revised: 11 December 2019
Accepted: 3 January 2020
Published: 29 December 2020
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Authors |
| Marco De Renzi | |
| Department of Mathematics Waseda University Tokyo Japan |
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| Nathan Geer | |
| Department of Mathematics and
Statistics Utah State University Logan, UT United States |
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| Bertrand Patureau-Mirand | |
| UMR 6205, LMBA Université de Bretagne-Sud Vannes France |
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