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3-Dimensional TQFTs From Non-Semisimple Modular Categories
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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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Non-semisimple open-closed 3d TFT
A spherical finite tensor category with a modified trace gives a finite-dimensional open-closed 3d TFT via a new handlebody invariant and the universal construction.
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