Speaker: Francis Bonahon, University of Southern California
Title of talk: Local representations of thequantum Teichmüller space
Abstract: Thequantum Teichmüller space of a punctured surface is a purelycombinatorial/algebraic object associated to this surface. Weinvestigate a certain type of representations of the correspondingalgebra, called local representations. These are essentially classifiedby group homomorphisms from the fundamental group of the surface to theisometry group of hyperbolic 3-space. Using hyperbolic metrics on3-manifolds fibering over the circle, we use this construction toextract invariants of diffeomorphisms of surfaces.