## Geometry & Topology

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

Daniel Groves

#### 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
Accepted: 3 December 2005
First available in Project Euclid: 20 December 2017

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

#### 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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