Homology stability for outer automorphism groups of free groups
Abstract
We prove that the quotient map from Aut(Fn) to Out(Fn) induces an isomorphism on homology in dimension i for n at least 2i+4. This corrects an earlier proof by the first author and significantly improves the stability range. In the course of the proof, we also prove homology stability for a sequence of groups which are natural analogs of mapping class groups of surfaces with punctures. In particular, this leads to a slight improvement on the known stability range for Aut(Fn), showing that its i-th homology is independent of n for n at least 2i+2.
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