In this class we will cover some of the tools, techniques, and groups central to the study of geometric group theory. After introducing the basic concepts (groups and metric spaces), we will branch out and sample different topics in geometric group theory based on the interest of the participants.
To learn and understand a wide range of tools and groups central to the field of geometric group theory.
Possible topics include: properties of free groups and groups acting on trees, large scale geometric invariants (Dehn functions, hyperbolicity, ends of groups, asymptotic dimension, growth of groups), and examples of notable and interesting groups (Coxeter groups, right-angled Artin groups, lamplighter groups, Thompson's group, mapping class groups, and braid groups).
The topics will be chosen from "Office Hours with a Geometric Group Theorist" edited by Matt Clay and Dan Margalit.
Voraussetzungen / Besonderes
One should be familiar with the basics of groups, metric spaces, and topology (should be familiar with the fundamental group).