Algebraic & Geometric Topology 8 (2008) 2131–2146

DOI: 10.2140/agt.2008.8.2131

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

Primary: 20F65, 57M07

References

Publication

Received: 29 July 2008
Revised: 1 October 2008
Accepted: 25 October 2008
Published: 10 November 2008

Authors