
Math 6843 Geometric Group Theory
Spring 2000
Information and Messages
 The Math 6843 course announcement.
 Math 6843 grading policy.
 Office hours are by appointment or email.
 List of topics. Current one is highlighted.
 Infinite groups as geometric objects.
 Word metric, Cayley graph, examples
 Quasi isometry, geodesic spaces, path metric, Hopf Rinow theorem,
Milnor theorem
 Statement of some q.i. classification and rigidity results
 some q.i. invariants in group theory
 Hyperbolic groups.
 Motivation/Background:
 word problem in free groups
 Dehn's algorithm for
closed surface groups
 basic geometry of hyperbolic plane and hyperbolic
3space
 Deltahyperbolic metric spaces:
 various definitions
 divergence of geodesics
 intro to the boundary
 Hyperbolic groups:
 various defintions
 IP inequalities, Dehn's algorithm
 basic properties
 CAT(0) and CAT(1) spaces and groups.
 Definitions and basic properties
 Constructing CAT(0) groups
