Groups and Dynamics Seminar

Date: December 8, 2021

Time: 3:00PM - 4:00PM

Location: online

Speaker: Mark Pengitore, University of Virginia

Title: Coarse embeddings and homological filling functions

Abstract: This work is joint with Rob Kropholler. In this talk, we will relate homological filling functions with coarse embeddings. In particular, we will demonstrate that a coarse embedding of a group into a group of geometric dimension 2 induces an inequality on homological Dehn functions in dimension 2. As an application of this, we are able to show that if a finitely presented group coarsely embeds into a hyperbolic group of geometric dimension 2, then it is hyperbolic. Another application is a characterization of subgroups of groups with quadratic Dehn function. If there is enough time, we will talk about various higher dimensional generalizations of our main result.