A Caltech Library Service

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. doi:10.2140/gt.2005.9.2319.

PDF - Published Version
See Usage Policy.

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


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.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
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.
Funding AgencyGrant Number
Subject Keywords:Relatively hyperbolic groups, limit groups, R–trees
Issue or Number:54
Classification Code:AMS subject classification. Primary: 20F65. Secondary: 20F67, 20E08, 57M07.
Record Number:CaltechAUTHORS:GROgt05
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1177
Deposited By: Archive Administrator
Deposited On:02 Jan 2006
Last Modified:08 Nov 2021 19:08

Repository Staff Only: item control page