Stable homology of automorphism groups of free groups

Soren Galatius, Stanford University

Let Aut(F_n) be the automorphism group of a free group on n generators. It is known that group homology H_k(Aut(F_n)) is independent of n as long as n > 2k+1 (by a theorem of Hatcher and Vogtmann). I will prove that in this stable range, group homology of Aut(F_n) is isomorphic to group homology of the symmetric group S_n. Consequently the rational homology of Aut(F_n) is trivial in the stable range. The proof will use the theory of metric graphs (in particular the contractibility of Culler-Vogtmann's "Outer Space") to translate the statement into a statement that can be proved using homotopy theoretic methods. arXiv: math.AT/0610216.