## Algebraic & Geometric Topology

### Automorphisms of free groups with boundaries

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 4, Number 1 (2004), 543-569.

Dates
Revised: 8 July 2004
Accepted: 9 July 2004
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.agt/1513882487

Digital Object Identifier
doi:10.2140/agt.2004.4.543

Mathematical Reviews number (MathSciNet)
MR2077676

Zentralblatt MATH identifier
1054.20023

#### Citation

Jensen, Craig; Wahl, Nathalie. Automorphisms of free groups with boundaries. Algebr. Geom. Topol. 4 (2004), no. 1, 543--569. doi:10.2140/agt.2004.4.543. https://projecteuclid.org/euclid.agt/1513882487

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