Algebraic & Geometric Topology

Automorphisms of free groups with boundaries

Craig Jensen and Nathalie Wahl

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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
Received: 26 February 2004
Revised: 8 July 2004
Accepted: 9 July 2004
First available in Project Euclid: 21 December 2017

Permanent link to this document
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

Subjects
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20F28: Automorphism groups of groups [See also 20E36]
Secondary: 20F05: Generators, relations, and presentations

Keywords
automorphism groups classifying spaces.

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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