Large scale geometry of commutator subgroups

Details Large scale geometry of commutator subgroups Large scale geometry of commutator subgroups

2008-07-29

arxiv.org/abs/0807.4704v2

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

Mathematics

Group Theory

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

Scientific paper

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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