Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 4, Number 2 (2004), 1253-1272.
Homology stability for outer automorphism groups of free groups
We prove that the quotient map from to induces an isomorphism on homology in dimension for at least . 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 , showing that its homology is independent of for at least .
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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