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.