Deforming cubulations

Speaker: Mark Hagen from University of Bristol

Abstract: Many hyperbolic groups admit proper, cocompact actions on CAT(0) cube complexes (which are in several senses “high-dimensional trees”). The reason for the ubiquity of these actions is a result, due to Sageev, that converts a nice enough collection of bipartitions of a group G into a CAT(0) cube complex. Most famously, if G is the fundamental group of a closed hyperbolic 3-manifold M, then a result of Kahn-Markovic provides enough immersed subsurfaces in M to endow G (via a general criterion by Bergeron-Wise) with a proper cocompact action on a cube complex. My goal is to explain the following results — joint work with Elia Fioravanti — about a one-ended hyperbolic group G that admits a proper cocompact action on a CAT(0) cube complex: first, if G has such an action, it has infinitely many essentially different ones, and second, it has such an action with a single orbit of hyperplanes.

Time: July 1st, Tuesday, 8pm

Location: Online
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