Geodesic
Homology stability for outer automorphism groups of free groups
Hatcher, Allen1 ; Vogtmann, Karen1
1Department of Mathematics, Cornell University, Ithaca NY 14853-4201, USA
Algebraic and Geometric Topology, Tome 4 (2004) no. 2, pp. 1253-1272
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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.

DOI : 10.2140/agt.2004.4.1253
Keywords: automorphisms of free groups, homology stability

Hatcher, Allen  1   ; Vogtmann, Karen  1

1 Department of Mathematics, Cornell University, Ithaca NY 14853-4201, USA 
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Hatcher, Allen; Vogtmann, Karen. Homology stability for outer automorphism groups of free groups. Algebraic and Geometric Topology, Tome 4 (2004) no. 2, pp. 1253-1272. doi: 10.2140/agt.2004.4.1253

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