Volume 4, issue 2 (2004)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Homology stability for outer automorphism groups of free groups

Allen Hatcher and Karen Vogtmann

Algebraic & Geometric Topology 4 (2004) 1253–1272

Erratum: Algebraic & Geometric Topology 6 (2006) 573–579

arXiv: math.GT/0406377

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 ith homology is independent of n for n at least 2i + 2.

Keywords
automorphisms of free groups, homology stability
Mathematical Subject Classification 2000
Primary: 20F65
Secondary: 20F28, 57M07
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Publication
Received: 28 June 2004
Accepted: 7 December 2004
Published: 24 December 2004
Authors
Allen Hatcher
Department of Mathematics
Cornell University
Ithaca NY 14853-4201
USA
Karen Vogtmann
Department of Mathematics
Cornell University
Ithaca NY 14853-4201
USA