3-Dimensional TQFTs From Non-Semisimple Modular Categories

Marco De Renzi; Azat M. Gainutdinov; Nathan Geer; Bertrand Patureau-Mirand; Ingo Runkel

doi:10.1007/s00029-021-00737-z

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arXiv · 1912.02063

3-Dimensional TQFTs From Non-Semisimple Modular Categories

Marco De Renzi·Azat M. Gainutdinov·Nathan Geer·Bertrand Patureau-Mirand·Ingo Runkel

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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.

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BibTeX RIS

Marco De Renzi, Azat M. Gainutdinov, Nathan Geer, Bertrand Patureau-Mirand, Ingo Runkel. 2019-12-04. 3-Dimensional TQFTs From Non-Semisimple Modular Categories. https://doi.org/10.1007/s00029-021-00737-z

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