3-Dimensional TQFTs From Non-Semisimple Modular Categories
Geometric Topology
2022-09-20 v3 High Energy Physics - Theory
Quantum Algebra
Abstract
We use modified traces to renormalize Lyubashenko's closed 3-manifold invariants coming from twist non-degenerate finite unimodular ribbon categories. Our construction produces new topological invariants which we upgrade to 2+1-TQFTs under the additional assumption of factorizability. The resulting functors provide monoidal extensions of Lyubashenko's mapping class group representations, as discussed in arXiv:2010.14852. This general framework encompasses important examples of non-semisimple modular categories coming from the representation theory of quasi-Hopf algebras, which were left out of previous non-semisimple TQFT constructions.
Cite
@article{arxiv.1912.02063,
title = {3-Dimensional TQFTs From Non-Semisimple Modular Categories},
author = {Marco De Renzi and Azat M. Gainutdinov and Nathan Geer and Bertrand Patureau-Mirand and Ingo Runkel},
journal= {arXiv preprint arXiv:1912.02063},
year = {2022}
}
Comments
49 pages; v3: added pictures and references