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, 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.

49 pages; v3: added pictures and references

References in corpus (4)

• Mapping Class Group Representations From Non-Semisimple TQFTs
• Hopf algebras and finite tensor categories in conformal field theory
• Extended TQFTs From Non-Semisimple Modular Categories
• Monadic cointegrals and applications to quasi-Hopf algebras

Cited by in corpus (21)

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• Extended TQFTs From Non-Semisimple Modular Categories
• Constructing non-semisimple modular categories with local modules
• Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups
• Reshetikhin-Turaev TQFTs close under generalised orbifolds
• Monadic cointegrals and applications to quasi-Hopf algebras
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• Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras
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• Non-Semisimple 3-Manifold Invariants Derived From the Kauffman Bracket
• Kerler-Lyubashenko Functors on 4-Dimensional 2-Handlebodies
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