3-Dimensional TQFTs from Non-Semisimple Modular Categories

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, to be discussed in a separate paper. 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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Submitted on : Tuesday, January 7, 2020 - 9:15:49 PM
Last modification on : Thursday, January 23, 2020 - 1:35:34 AM

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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. 2020. ⟨hal-02431445⟩



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