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Large scale geometry of commutator subgroups
2008
Algebraic and Geometric Topology
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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.
doi:10.2140/agt.2008.8.2131
fatcat:k3k62i4zkff23crqbde73kjety