Homology stability for outer automorphism groups of free groups

Details Homology stability for outer automorphism groups of free groups Homology stability for outer automorphism groups of free groups

2004-06-18

arxiv.org/abs/math/0406377v2

Algebr. Geom. Topol. 4 (2004) 1253-1272

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-54.abs.html

Scientific paper

We prove that the quotient map from Aut(F_n) to Out(F_n) 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(F_n), showing that its i-th homology is independent of n for n at least 2i+2.

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