Homology stability for outer automorphism groups of free groups
Geometric Topology
2014-10-01 v2
Abstract
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.
Cite
@article{arxiv.math/0406377,
title = {Homology stability for outer automorphism groups of free groups},
author = {Allen Hatcher and Karen Vogtmann},
journal= {arXiv preprint arXiv:math/0406377},
year = {2014}
}
Comments
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-54.abs.html