State sum invariants of combed 3-manifolds (Alexis Virelizier, Université de Lille)

20.02.2020 14:15

A fundamental example of a quantum invariant of 3-manifolds is the Turaev-Viro invariant defined in the 90's. This approach (in its general form due to Barrett and Westbury) uses a spherical fusion category as the main ingredient and consists in a state sum on skeletons of 3-manifolds whose vertices are colored by the 6j-symbols of the category. We extend the Turaev-Viro construction to combed 3-manifolds (that is, to 3-manifolds endowed with a nowhere-zero vector field) using pivotal fusion categories (not necessarily spherical). Our construction consists in a state sum on branched spines of combed 3-manifolds, which are a combinatorial presentation of combed 3-manifolds developed by Ishii, Benedetti, and Petronio.

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