Non-Semisimple Quantum Invariants and TQFTs from Small and Unrolled Quantum Goups
Geometric Topology
2021-01-06 v2 Quantum Algebra
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.
Keywords
Cite
@article{arxiv.1812.10685,
title = {Non-Semisimple Quantum Invariants and TQFTs from Small and Unrolled Quantum Goups},
author = {Marco De Renzi and Nathan Geer and Bertrand Patureau-Mirand},
journal= {arXiv preprint arXiv:1812.10685},
year = {2021}
}
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33 pages