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

Costantino, Francesco; Geer, Nathan; Patureau-Mirand, Bertrand; Virelizier, Alexis

Document type :

Pré-publication ou Document de travail

Title :

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

Author(s) :

Costantino, Francesco [Auteur]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Geer, Nathan [Auteur]
Patureau-Mirand, Bertrand [Auteur]
Laboratoire de Mathématiques de Bretagne Atlantique [LMBA]
Virelizier, Alexis [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Publication date :

2023-02-09

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Comment :

10 pages

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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2302.04509
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