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. https://resolver.caltech.edu/CaltechAUTHORS:20170408-171448676
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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.
| Item Type: | Article | |||||||||
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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 | |||||||||
| DOI: | 10.2140/agt.2008.8.2131 | |||||||||
| Record Number: | CaltechAUTHORS:20170408-171448676 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170408-171448676 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 76311 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | 1Science Import | |||||||||
| Deposited On: | 13 Mar 2018 17:21 | |||||||||
| Last Modified: | 15 Nov 2021 16:59 |
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