Geometric group theory is a relatively new field of mathematics, originating less than 40 years ago. It encompasses the area which used to be known as “Topological Methods in Group Theory”. The idea is to study infinite groups by studying their actions on metric spaces and other topological spaces. When dealing with actions on metric spaces the basic notion of equivalence is that of “quasi-isometry’'.

Class: MoWeFr Time: 10:20 - 11:15 AM

Class room: EC 209

Call number: 33453

Course webpage: https://people.math.osu.edu/davis.12/courses/8800/8800.html

Lecturer: Michael Davis

Office: MW (Math Tower) 616

E-mail: davis.12@osu.edu

Phone: 292-4886

Office hours: MoWeFr 11:20 - 12:00 AM

List of topics (pdf file)

Other links: Kevin Whyte, Bruce Kleiner

Article by J. Behrstock

Scott-Wall article, Bowditch Notes , Milnor article

MSRI notes on hyperbolic groups, Serre-Trees,

Thurston on orbifolds

Topics will include:

Cayley graphs, growth of groups, groups up to quasi-isometry

Actions on low dimensional spaces: actions on trees, fundamental groups of surfaces

Spaces of nonpositive curvature and negative curvature, hyperbolic space, hyperbolic groups

Examples: lattices in Lie groups, the mapping class group, Coxeter groups, braid groups, Artin groups

Prerequisite: Math 6810, Algebraic Topology I (particularly knowledge about the fundamental group and covering spaces)

Possible text: M. Bridson and A. Haefliger,