Approximating hyperbolic lattices by cubulations

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• Eduardo Reyes, Max Planck Institute Bonn
• Friday 17 November 2023, 13:45-14:45
• MR13.

If you have a question about this talk, please contact Macarena Arenas.

The fundamental group of an n-dimensional closed hyperbolic manifold admits a natural isometric action on the hyperbolic space Hⁿ. When n is at most 3 or the manifold is arithmetic of simplest type, the group also admits many geometric actions on CAT cube complexes. I will talk about a joint work with Nic Brody in which we approximate the asymptotic geometry of the action on Hⁿ by the 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. In the 3-dimensional case, we also use some results about minimal surfaces in hyperbolic 3-manifolds.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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