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

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.