Volume 8, issue 4 (2008)

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Large scale geometry of commutator subgroups

Danny Calegari and Dongping Zhuang

Algebraic & Geometric Topology 8 (2008) 2131–2146
Abstract

Let G be a finitely presented group, and G its commutator subgroup. Let C be the Cayley graph of G with all commutators in G as generators. Then C is large scale simply connected. Furthermore, if G is a torsion-free nonelementary word-hyperbolic group, C is one-ended. Hence (in this case), the asymptotic dimension of C is at least 2.

Keywords
commutator subgroup, large-scale connectedness, commutator length, hyperbolic group
Mathematical Subject Classification 2000
Primary: 20F65, 57M07
References
Publication
Received: 29 July 2008
Revised: 1 October 2008
Accepted: 25 October 2008
Published: 10 November 2008
Authors
Danny Calegari
Department of Mathematics
California Institute of Technology
Pasadena CA 91125
USA
http://www.its.caltech.edu/~dannyc
Dongping Zhuang
California Institute of Technology
Department of Mathematics
Pasadena, CA 91125
USA