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arXiv · 0807.4704

Large scale geometry of commutator subgroups

Danny Calegari·Dongping Zhuang
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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. 2008-10-27. Large scale geometry of commutator subgroups. https://doi.org/10.2140/agt.2008.8.2131

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