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2004 Homology stability for outer automorphism groups of free groups
Allen Hatcher, Karen Vogtmann
Algebr. Geom. Topol. 4(2): 1253-1272 (2004). DOI: 10.2140/agt.2004.4.1253

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.

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Allen Hatcher. Karen Vogtmann. "Homology stability for outer automorphism groups of free groups." Algebr. Geom. Topol. 4 (2) 1253 - 1272, 2004. https://doi.org/10.2140/agt.2004.4.1253

Information

Received: 28 June 2004; Accepted: 7 December 2004; Published: 2004
First available in Project Euclid: 21 December 2017

zbMATH: 1093.20020
MathSciNet: MR2113904
Digital Object Identifier: 10.2140/agt.2004.4.1253

Subjects:
Primary: 20F65
Secondary: 20F28, 57M07

Rights: Copyright © 2004 Mathematical Sciences Publishers

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Vol.4 • No. 2 • 2004
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