Algebraic & Geometric Topology

Homology stability for outer automorphism groups of free groups

Allen Hatcher and Karen Vogtmann

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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.

Article information

Algebr. Geom. Topol., Volume 4, Number 2 (2004), 1253-1272.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 20F28: Automorphism groups of groups [See also 20E36] 57M07: Topological methods in group theory

automorphisms of free groups homology stability


Hatcher, Allen; Vogtmann, Karen. Homology stability for outer automorphism groups of free groups. Algebr. Geom. Topol. 4 (2004), no. 2, 1253--1272. doi:10.2140/agt.2004.4.1253.

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