## Algebraic & Geometric Topology

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

#### 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 $2i+2$.

#### Article information

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

Dates
Accepted: 7 December 2004
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.agt/1513882551

Digital Object Identifier
doi:10.2140/agt.2004.4.1253

Mathematical Reviews number (MathSciNet)
MR2113904

Zentralblatt MATH identifier
1093.20020

#### Citation

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. https://projecteuclid.org/euclid.agt/1513882551

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