Non-Semisimple Quantum Invariants and TQFTs from Small and Unrolled Quantum Goups

Marco De Renzi; Nathan Geer; Bertrand Patureau-Mirand

doi:10.2140/agt.2020.20.3377

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arXiv · 1812.10685

Non-Semisimple Quantum Invariants and TQFTs from Small and Unrolled Quantum Goups

Marco De Renzi·Nathan Geer·Bertrand Patureau-Mirand

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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 non-semisimple 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. 2018-12-27. Non-Semisimple Quantum Invariants and TQFTs from Small and Unrolled Quantum Goups. https://doi.org/10.2140/agt.2020.20.3377

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