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Journal Articles Selecta Math. Year : 2022

3-Dimensional TQFTs from non-semisimple modular categories

Marco de Renzi
Azat M. Gainutdinov
Nathan Geer
  • Function : Author
Ingo Runkel
  • Function : Author

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 De Renzi et al. (Commun Contemp Math, 2021. https://doi.org/10.1142/S0219199721500917). 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.

Dates and versions

hal-02431445 , version 1 (07-01-2020)

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Marco de Renzi, Azat M. Gainutdinov, Nathan Geer, Bertrand Patureau-Mirand, Ingo Runkel. 3-Dimensional TQFTs from non-semisimple modular categories. Selecta Math., 2022, 28 (2), pp.42. ⟨10.1007/s00029-021-00737-z⟩. ⟨hal-02431445⟩
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