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Large scale geometry of commutator subgroups

Calegari, Danny and Zhuang, Dongping (2008) Large scale geometry of commutator subgroups. Algebraic & Geometric Topology, 8 (4). pp. 2131-2146. ISSN 1472-2747. doi:10.2140/agt.2008.8.2131.

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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.

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Additional Information:© Mathematical Sciences Publishers. Received: 29 July 2008. Revised: 1 October 2008. We would like to thank Koji Fujiwara for some useful conversations. We would also like to thank the anonymous referee for a careful reading, and many useful comments. Danny Calegari was partially funded by NSF grant DMS 0707130.
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Subject Keywords:commutator subgroup, large-scale connectedness, commutator length, hyperbolic group
Issue or Number:4
Classification Code:Mathematical Subject Classification 2000 Primary: 20F65, 57M07
Record Number:CaltechAUTHORS:20170408-171448676
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:76311
Deposited By: 1Science Import
Deposited On:13 Mar 2018 17:21
Last Modified:15 Nov 2021 16:59

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