#### 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.

Notes on file formats
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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