Geometry & Topology

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

Daniel Groves

Full-text: Open access

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.

Article information

Source
Geom. Topol., Volume 9, Number 4 (2005), 2319-2358.

Dates
Received: 15 March 2005
Accepted: 3 December 2005
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799682

Digital Object Identifier
doi:10.2140/gt.2005.9.2319

Mathematical Reviews number (MathSciNet)
MR2209374

Zentralblatt MATH identifier
1100.20032

Subjects
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 20F67: Hyperbolic groups and nonpositively curved groups 20E08: Groups acting on trees [See also 20F65] 57M07: Topological methods in group theory

Keywords
relatively hyperbolic groups limit groups $\mathbb{R}$–trees

Citation

Groves, Daniel. Limit groups for relatively hyperbolic groups, II: Makanin-Razborov diagrams. Geom. Topol. 9 (2005), no. 4, 2319--2358. doi:10.2140/gt.2005.9.2319. https://projecteuclid.org/euclid.gt/1513799682


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