Geodesic
Large scale geometry of commutator subgroups
Calegari, Danny1 ; Zhuang, Dongping2
1Department of Mathematics, California Institute of Technology, Pasadena CA 91125, USA
2California Institute of Technology, Department of Mathematics, Pasadena, CA 91125, USA
Algebraic and Geometric Topology, Tome 8 (2008) no. 4, pp. 2131-2146
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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
Keywords: commutator subgroup, large-scale connectedness, commutator length, hyperbolic group

Calegari, Danny  1   ; Zhuang, Dongping  2

1 Department of Mathematics, California Institute of Technology, Pasadena CA 91125, USA
2 California Institute of Technology, Department of Mathematics, Pasadena, CA 91125, USA 
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Calegari, Danny; Zhuang, Dongping. Large scale geometry of commutator subgroups. Algebraic and Geometric Topology, Tome 8 (2008) no. 4, pp. 2131-2146. doi: 10.2140/agt.2008.8.2131

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