Large scale geometry of commutator subgroups
Group Theory
2014-10-01 v2 Geometric Topology
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.
Cite
@article{arxiv.0807.4704,
title = {Large scale geometry of commutator subgroups},
author = {Danny Calegari and Dongping Zhuang},
journal= {arXiv preprint arXiv:0807.4704},
year = {2014}
}
Comments
12 pages, 2 figures; version 2 incorporates referee's comments