A manifestly Morita-invariant construction of Turaev-Viro invariants (David Jaklitsch)

Orateur : David Jaklitsch

Lieu : salle des Séminaires M3

Résumé :

The purpose of the talk is to recall the construction of the Turaev-Viro invariant for a closed oriented three-dimensional manifold M. We present a different state sum construction that assigns a scalar to a skeleton of M. The input datum is the pivotal bicategory Mod^sph(A) of spherical module categories over a spherical fusion category A.  The interplay of algebraic structures in this pivotal bicategory with moves of skeleta ensures that our state sum is independent of the skeleton on the manifold. As it will turn out, the invariant assigned to M recovers the value of the Turaev-Viro construction based on A, thereby showing the intrinsic pivotal Morita-invariance of the state sum model.