# Geometric Analysis and Topology Seminar

#### Stable Homology of Aut(F_N)

Speaker: Soren Galatius, Stanford

Location: Warren Weaver Hall 813

Date: Friday, April 28, 2006, 4 p.m.

Synopsis:

Let $$\mathrm{Aut}(F_n)$$ denote the automorphism group of a free group on $$n$$ generators. It is known that $$H_k(\mathrm{Aut}(F_n))$$ is independent of $$n$$ as long as $$n >> k$$. There is a natural homomorphism from the symmetric group $$S_n$$ to $$\mathrm{Aut}(F_n)$$, I will sketch a proof that it induces an isomorphism from $$H_k(S_n)$$ to $$H_k(\mathrm{Aut}(F_n))$$ for $$n >> k$$. An important point of view here is that the classifying space $$B \mathrm{Aut}(F_n)$$ can be thought of as a moduli space of metric graphs, i.e. graphs equipped with metrics, considered up to isometry.