Mathematics Colloquium: Groups of Proper Homotopy Equivalences of Graphs

Speaker:  Hannah Hoganson, University of Maryland

Title:  Groups of Proper Homotopy Equivalences of Graphs

Abstract :  Mapping class groups are classical objects of study in geometric group theory that record algebraic information about the symmetries of a geometric object. We will start with an overview of ``big and small" mapping class groups in dimensions 0,1, and 2, before focusing in on the mapping class group of a locally finite, infinite graph, which corresponds to the big group in dimension 1. These groups were introduced by Algom-Kfir and Bestvina as a proposed big analog of symmetry groups of free groups. These big groups are not finitely generated, so classical tools and techniques don't apply. Instead, we turn to descriptive set theoretic techniques of Rosendal to study their large-scale geometry. This is joint work with George Domat and Sanghoon Kwak.  

Time:  Friday, September 22, 3:30pm – 4:20pm

Place:  Exploratory Hall, room 4106

Zoom and In-person