Algebraic & Geometric Topology 4 (2004) 1253–1272

DOI: 10.2140/agt.2004.4.1253

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

arXiv: math.GT/0406377

Abstract

We prove that the quotient map from Aut(F_n) to Out(F_n) 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(F_n), 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

Primary: 20F65

Secondary: 20F28, 57M07

References

Forward citations

Publication

Received: 28 June 2004
Accepted: 7 December 2004
Published: 24 December 2004

Authors