Algebraic and Geometric Topology 4 (2004), paper no. 54, pages 1253-1272.

Homology stability for outer automorphism groups of free groups

Allen Hatcher, Karen Vogtmann

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 i-th homology is independent of n for n at least 2i+2.

Keywords. Automorphisms of free groups, homology stability

AMS subject classification. Primary: 20F65. Secondary: 20F28, 57M07.

DOI: 10.2140/agt.2004.4.1253

E-print: arXiv:math.GT/0406377

Submitted: 28 June 2004. Accepted: 7 December 2004. Published: 24 December 2004.

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Allen Hatcher, Karen Vogtmann
Department of Mathematics, Cornell University
Ithaca, NY 14853-4201, USA

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