Abstract: Let Aut(F_n) denote the automorphism group of a free group on n letters.
I will sketch a proof that H_k(Aut(F_n);Q) = 0 when n >> k, and in fact
determine the integral homology. The proof introduces a certain "graph
cobordism category". Objects are natural numbers, and the space of
morphisms from n to m is the space of finite graphs with n+m marked
leaves, topologized similarly to Culler-Vogtmann's Outer Space. Gromov's
h-principle is used to determine the homotopy type of the classifying
space of the category.