#### Volume 4, issue 1 (2004)

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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 ${A}_{n,k}$ 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