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 3-space
    • 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