Math 8800, Topics in Topology: Introduction to Geometric Group Theory

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:

Lecturer:   Michael Davis
Office:   MW (Math Tower) 616
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, Metric spaces of non-positive curvature, Springer-Verlag, Berlin and New York, 1999.  ISSN 0072-7830,  ISBN 3-540-64324-9.