The Teichmüller TQFT volume conjecture for twist knots

Topologie

Lieu: 
Salle Duhem M3
Orateur: 
Fathi Ben Aribi
Affiliation: 
Université Catholique de Louvain
Dates: 
Vendredi, 24 Janvier, 2020 - 14:00 - 15:00
Résumé: 

(joint project with E. Piguet-Nakazawa and F. Guéritaud)

In 2011, Andersen and Kashaev defined an infinite-dimensional TQFT from quantum Teichmüller theory. This Teichmüller TQFT yields an invariant of triangulated 3-manifolds, in particular knot complements.

The associated volume conjecture states that the Teichmüller TQFT of an hyperbolic knot complement contains the volume of the knot as a certain asymptotical coefficient, and Andersen-Kashaev proved this conjecture for the first two hyperbolic knots.

In this talk, after a brief history of quantum knot invariants and volume conjectures, I will present the construction of the Teichmüller TQFT and how we approached its volume conjecture for the infinite family of twist knots, by constructing new geometric triangulations of the knot complements.

The construction and properties of these triangulations will only be summarized in the present talk but will be more developed in a previous talk at the Geometry and Dynamics seminar.