Topics in Topology: Geometric Group Theory
Spring 2010
Course description:
This course will be intended as a survey of various important topics in geometric group theory. I aim to discuss the following:
- group actions, groups as metric spaces
- group splittings and accessibility: Bass-Serre theory from [Scott-Wall], Stallings' Theorem
- CAT(0) spaces and groups from [Bridson-Haefliger]
- Gromov hyperbolic spaces and groups from [Bridson-Haefliger]
As time and class interest permit, we may also get to some of:
- finiteness properties
- quasi-isometry invariants, e.g. Gromov's Polynomial Growth Theorem
- boundaries at infinity
- asymptotic cones
- mapping class groups
Grades will probably be based on attendance and some homework assignments.
Prerequisites: 500-level course on group theory and Math 513 or equivalent.