arXiv:0807.4704 Abstract | arXiv Analytics

arXiv:0807.4704 [math.GR]Abstract References Reviews Resources

Large scale geometry of commutator subgroups

Published 2008-07-29, updated 2008-10-27Version 2

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.

Comments: 12 pages, 2 figures; version 2 incorporates referee's comments

Journal: Algebr. Geom. Topol. 8 (2008) no. 4, 2131-2146

Categories: math.GR, math.GT

Subjects: 20F65, 57M07

Keywords: large scale geometry, commutator subgroup, torsion-free nonelementary word-hyperbolic group, asymptotic dimension, cayley graph

Tags: journal article

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