Paper published by Algebraic and Geometric Topology

From: Geometry and Topology Journal (gt_at_maths.warwick.ac.uk)
Date: 12/24/04

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    Date: Fri, 24 Dec 2004 18:30:05 +0000 (UTC)

    The following paper has been published:

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

    URL:
    http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-54.abs.html

    Title:
    Homology stability for outer automorphism groups of free groups

    Author(s):
    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.

    AMS Classification Numbers. Primary: 20F65
    Secondary: 20F28, 57M07

    Keywords:
    Automorphisms of free groups, homology stability

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

    Author(s) address(es):
    Department of Mathematics, Cornell University
    Ithaca, NY 14853-4201, USA
    Email: hatcher@math.cornell.edu, vogtmann@math.cornell.edu

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