Stable homology of automorphism groups of free groups

Abstract

Homology of the group Aut(Fn) of automorphisms of a free group on n generators is known to be independent of n in a certain stable range. Using tools from homotopy theory, we prove that in this range it agrees with homology of symmetric groups. In particular, Aut(Fn) has no stable rational homology, settling a conjecture of Hatcher and Vogtmann.

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