Automorphisms of free groups with boundaries

Jensen, Craig; Wahl, Nathalie

doi:10.2140/agt.2004.4.543

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Automorphisms of free groups with boundaries

Craig A Jensen and Nathalie Wahl

Algebraic & Geometric Topology 4 (2004) 543–569

DOI: 10.2140/agt.2004.4.543

arXiv: math.GT/0402166

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.

Mathematical Subject Classification 2000

Primary: 20F65, 20F28

Secondary: 20F05

References

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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

Volume 4, issue 1 (2004)