Homological Stability of Automorphism Groups of Free Groups

Geometry Topology Student Seminar
Wednesday, September 14, 2016 - 2:05pm
1 hour (actually 50 minutes)
Skiles 006
Georgia Tech
Many algebraic results about free groups can be proven by considering a topological model suggested by Whitehead: glue two handlebodies trivially along their boundary to obtain a closed 3-manifold with free fundamental group. The complex of embedded spheres in the manifold gives a combinatorial model for the automorphism group of the free group. We will discuss how Hatcher uses this complex to show that the homology of the automorphism group is (eventually) independent of the rank of the free group.