Large scale geometry of commutator subgroups
arXiv:0807.4704 · 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.
12 pages, 2 figures; version 2 incorporates referee's comments