The space of metric structures on hyperbolic groups
20.30 SR 2.058
Teichmuller space is a classical construction, which for a given closed hyperbolic surface, parameterizes the geometric actions of its fundamental group on the hyperbolic plane. I will talk about a generalization of this space, where for an arbitrary hyperbolic group we consider a moduli space of its geometric actions on Gromov hyperbolic spaces. Equipped with a natural Lipschitz metric, this space is contractible and geodesic, and when the group is torsion-free, has a “thick” part that is cocompact for the isometric action of the outer automorphism group. This is joint work with Stephen Cantrell.