#### Volume 8, issue 4 (2008)

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 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
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 ${G}^{\prime }$ its commutator subgroup. Let $C$ be the Cayley graph of ${G}^{\prime }$ 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