Groves, Daniel (2005) Limit groups for relatively hyperbolic groups, II: Makanin-Razborov diagrams. Geometry and Topology, 9 (54). pp. 2319-2358. ISSN 1465-3060. doi:10.2140/gt.2005.9.2319. https://resolver.caltech.edu/CaltechAUTHORS:GROgt05
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Abstract
Let Γ be a torsion-free group which is hyperbolic relative to a collection of free abelian subgroups. We construct Makanin–Razborov diagrams for Γ. We also prove that every system of equations over Γ is equivalent to a finite subsystem, and a number of structural results about Γ–limit groups.
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| Additional Information: | © 2005 Geometry & Topology Publications. Submitted to G&T on 15 March 2005. Paper accepted 3 December 2005. Paper published 21 December 2005. Proposed: Benson Farb; Seconded: Walter Neumann, Martin Bridson I would like to thank Zlil Sela for providing me with the proof of [32, Proposition 1.21], which is repeated in the proof of Proposition 5.14 in this paper. I would also like to thank the referee for correcting a number of mistakes in earlier versions of this paper, in particular the use of the bending moves in shortening quotients, and for his/her careful reading(s) and numerous comments, which have substantially improved the exposition of the results in this paper. This work was supported in part by NSF Grant DMS-0504251. | |||||||||
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| Subject Keywords: | Relatively hyperbolic groups, limit groups, R–trees | |||||||||
| Issue or Number: | 54 | |||||||||
| Classification Code: | AMS subject classification. Primary: 20F65. Secondary: 20F67, 20E08, 57M07. | |||||||||
| DOI: | 10.2140/gt.2005.9.2319 | |||||||||
| Record Number: | CaltechAUTHORS:GROgt05 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:GROgt05 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 1177 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Archive Administrator | |||||||||
| Deposited On: | 02 Jan 2006 | |||||||||
| Last Modified: | 08 Nov 2021 19:08 |
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