Stable Homology of Automorphism Groups of Free Groups

Soren Galatius

Stanford University

Brandeis University

Thursday, September 29, 2005

Talk at 4:30 p.m. in 317 Goldsmith Hall

Tea at 4:00 p.m. in 300 Goldsmith Hall

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.

Home Web page: Alexandru I. Suciu Posted: September 15, 2005
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