Algebraic and Geometric Topology 4 (2004), paper no. 25, pages 543-569.

Automorphisms of free groups with boundaries

Craig A. Jensen, Nathalie Wahl

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

Keywords. Automorphism groups, classifying spaces.

AMS subject classification. Primary: 20F65, 20F28. Secondary: 20F05.

DOI: 10.2140/agt.2004.4.543

E-print: arXiv:math.GT/0402166

Submitted: 26 February 2004. (Revised: 8 July 2004.) Accepted: 9 July 2004. Published: 15 July 2004.

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Craig A. Jensen, Nathalie Wahl
Department of Mathematics, University of New Orleans
New Orleans, LA 70148, USA
and
Department of Mathematics, University of Aarhus
Ny Munkegade 116, 8000 Aarhus, DENMARK
Email: jensen@math.uno.edu, wahl@imf.au.dk

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