WoG 2024 Talk 6.4: Eduardo Reyes - Approximating hyperbolic lattices by cubulations

Speaker: Eduardo Reyes
Institution: Yale University
Website: reyes-eduardo....
Title: Approximating hyperbolic lattices by cubulations
Abstract: The fundamental group of an $n$-dimensional closed hyperbolic manifold admits a natural isometric action on the hyperbolic space $\mathbb{H}^n$. 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 $\mathbb{H}^n$ 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.