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