Cornell Math - MATH 761, Fall 2003

MATH 757
Automorphisms of Free Groups
 (Fall 2003)

Instructor: Karen Vogtmann

Meeting Time & Room

This course will be an introduction to the study of automorphism groups of free groups, concentrating mainly on geometric and topological methods using the action of these groups on Outer space and its variations. We will begin with classical results of Nielsen, Magnus, Whitehead and Stallings, then proceed with the construction and exploration of Outer space.

Topics may include:

  • The spine of Outer space
  • Contractibility of Outer space
  • Local structure of the spine
  • Symmetries of outer space
  • Mapping class subgroups and Teichmuller subcomplexes
  • Isopermetric functions
  • Dynamics of the action of an automorphism
  • Train tracks and normal forms
  • Techniques for computing the homology of Out(F_n)
  • Homology stability theorems
  • Euler characteristic
  • Kontsevich's graph homology and Outer space
  • Morita traces