Nonsemisimple quantum invariants and TQFTs from small and unrolled quantum groups

De Renzi, Marco¹ ; Geer, Nathan² ; Patureau-Mirand, Bertrand³

¹Department of Mathematics, Waseda University, Tokyo, Japan
²Department of Mathematics and Statistics, Utah State University, Logan, UT, United States
³UMR 6205, LMBA, Université de Bretagne-Sud, Vannes, France

Algebraic and Geometric Topology, Tome 20 (2020) no. 7, pp. 3377-3422

Résumé

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.

Détail

DOI : 10.2140/agt.2020.20.3377

Classification : 57M27, 81R50
Keywords: nonsemisimple quantum invariants, nonsemisimple TQFTs, small quantum groups, unrolled quantum groups

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