Non compact 3-dimensional TQFTs from non-semisimple spherical categories.

23.05.2024 14:15

A chromatic category is a pivotal linear category endowed with a non-degenerate modified trace on the ideal of projective objects and with a chromatic map (which plays the role of the Kirby color in the Reshetikhin-Turaev surgery semisimple approach). For example, each spherical tensor category (in the sense of Etingof, Douglas et al.) is a chromatic category. We associate to any chromatic category a finite dimensional non-compact 3-dimensional TQFT. Its construction consists of assigning admissible skein modules to closed oriented surfaces and using Juhász's presentation of cobordisms. The resulting TQFT extends to a genuine one if and only if the chromatic category is semisimple with nonzero dimension (recovering then the Turaev-Viro TQFT). This is a joint work with Francesco Costantino, Nathan Geer, and Bertrand Patureau-Mirand.

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Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Topologie et Géométrie"

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