Math 6843 Geometric Group Theory
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,
- Statement of some q.i. classification and rigidity results
- some q.i. invariants in group theory
- Hyperbolic groups.
- word problem in free groups
- Dehn's algorithm for
closed surface groups
- basic geometry of hyperbolic plane and hyperbolic
- Delta-hyperbolic 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