Math 598, Introduction to geometric group theory.
Time: T/Th 1030-1150
Location: REC 317
Homework: Random suggested problems not to be graded.
The suggested textbooks are
(1) de la Harpe, Topics in geometric group theory.
(2) Bridson-Haefliger, Metric spaces of non-positive curvature.
(3) Lubotzky, Discrete groups, expander graphs, and invariant measures.
The coarse will loosely be divided into three broad modules:
- Basics in group theory. We will follow de la Harpe and some of Bridson-Haefliger. We will talk about free groups, free products, amalgamated free products, ping-pong lemma, Cayley graphs, word metrics, quasi-isometries, and group actions.
- Hyperbolic groups. Basic theory and examples. We will follow Bridson-Haefliger. We will talk about some motivational examples of hyperbolic groups and some general theory. This module will be some of a survey though many basic things will be rigorously established.
- Amenability and property T. We will talk about amenability and property T, two generalizations of compactness. Here, we will likely follow portions of Lubotzky (and also Margulis and Zimmer). Lubotzky's book suffices as a general reference.
At present, I plan to scan my lecture notes. I also plan to assign some problems for students to work. However, I do not plan on taking them up at any point though I could pose challenge problems that could earn a "reward" if successful done.