# 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.