Geometry & Topology, Vol. 9 (2005) Paper no. 54, pages 2319--2358.

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

Daniel Groves

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.

Keywords. Relatively hyperbolic groups, limit groups, R-trees

AMS subject classification. Primary: 20F65. Secondary: 20F67, 20E08, 57M07.

E-print: arXiv:math.GR/0503045

DOI: 10.2140/gt.2005.9.2319

Submitted to G&T on 15 March 2005. Paper accepted 3 December 2005. Paper published 21 December 2005.

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Daniel Groves
Department of Mathematics, California Institute of Technology
Pasadena, CA 91125, USA
Email: groves@caltech.edu

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