Volume 4, issue 1 (2004)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Automorphisms of free groups with boundaries

Craig A Jensen and Nathalie Wahl

Algebraic & Geometric Topology 4 (2004) 543–569

arXiv: math.GT/0402166

Abstract

The automorphisms of free groups with boundaries form a family of groups An,k closely related to mapping class groups, with the standard automorphisms of free groups as An,0 and (essentially) the symmetric automorphisms of free groups as A0,k. We construct a contractible space Ln,k on which An,k acts with finite stabilizers and finite quotient space and deduce a range for the virtual cohomological dimension of An,k. We also give a presentation of the groups and calculate their first homology group.

Keywords
automorphism groups, classifying spaces.
Mathematical Subject Classification 2000
Primary: 20F65, 20F28
Secondary: 20F05
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Publication
Received: 26 February 2004
Revised: 8 July 2004
Accepted: 9 July 2004
Published: 15 July 2004
Authors
Craig A Jensen
Department of Mathematics
University of New Orleans
New Orleans LA 70148
USA
Nathalie Wahl
Department of Mathematics
University of Aarhus
Ny Munkegade 116
8000 Aarhus
Denmark