#### Volume 9, issue 4 (2005)

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

### Daniel Groves

Geometry & Topology 9 (2005) 2319–2358
 arXiv: math.GR/0503045
##### 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, $\mathbb{R}$–trees
##### Mathematical Subject Classification 2000
Primary: 20F65
Secondary: 20F67, 20E08, 57M07