Joint IAS/PU Groups and Dynamics Seminar

The fundamental group of an n-dimensional closed hyperbolic manifold admits a natural isometric action on the hyperbolic space $H^n$. If n is at most 3 or the manifold is arithmetic of simplest type, then the group also admits many geometric actions on $CAT(0)$ cube complexes. I will talk about a joint work with Nic Brody in which we approximate the asymptotic geometry of the action on $H^n$ by actions on these complexes, solving a conjecture of Futer and Wise. The main tool is a codimension-1 generalization of the space of geodesic currents introduced by Bonahon.