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2008 Large scale geometry of commutator subgroups
Danny Calegari, Dongping Zhuang
Algebr. Geom. Topol. 8(4): 2131-2146 (2008). 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.

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Danny Calegari. Dongping Zhuang. "Large scale geometry of commutator subgroups." Algebr. Geom. Topol. 8 (4) 2131 - 2146, 2008. https://doi.org/10.2140/agt.2008.8.2131

Information

Received: 29 July 2008; Revised: 1 October 2008; Accepted: 25 October 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1195.20046
MathSciNet: MR2460882
Digital Object Identifier: 10.2140/agt.2008.8.2131

Subjects:
Primary: 20F65, 57M07

Rights: Copyright © 2008 Mathematical Sciences Publishers

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