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Limit groups for relatively hyperbolic groups, II: Makanin-Razborov diagrams

Groves, Daniel (2005) Limit groups for relatively hyperbolic groups, II: Makanin-Razborov diagrams. Geometry and Topology, 9 (54). pp. 2319-2358. ISSN 1465-3060. http://resolver.caltech.edu/CaltechAUTHORS:GROgt05

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Abstract

Let [Gamma] be a torsion-free group which is hyperbolic relative to a collection of free abelian subgroups. We construct Makanin–Razborov diagrams for [Gamma]. We also prove that every system of equations over [Gamma] is equivalent to a finite subsystem, and a number of structural results about [Gamma]–limit groups.


Item Type:Article
Additional Information: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. arXiv:math.GR/0503045
Subject Keywords:Relatively hyperbolic groups, limit groups, R–trees
Record Number:CaltechAUTHORS:GROgt05
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:GROgt05
Alternative URL:http://dx.doi.org/10.2140/gt.2005.9.2319
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:26 Dec 2012 08:43

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