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Pré-Publication, Document De Travail Année : 2023

Non compact (2+1)-TQFTs from non-semisimple spherical categories

Résumé

To every spherical tensor category (in the sense of Etingof, Douglas et al.) we define a finite dimensional non-compact (2+1)-TQFT (a TQFT for short). More generally, we define a TQFT for every pivotal category with non-degenerate m-trace and chromatic morphism. The TQFT of closed surfaces are the admissible skein modules (given in a joint preprint of the first three authors) and the underlying invariants of closed 3-manifolds of the TQFT are the generalized (non-semisimple) Turaev-Viro type invariants defined in arXiv:1809.07991. We expect that our construction is related to the general universal non semi-simple TQFT announced by Kevin Walker and David Reutter.

Dates et versions

hal-03988597 , version 1 (14-02-2023)

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Francesco Costantino, Nathan Geer, Bertrand Patureau-Mirand, Alexis Virelizier. Non compact (2+1)-TQFTs from non-semisimple spherical categories. 2023. ⟨hal-03988597⟩
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