The structure of limit groups over hyperbolic groups

@article{Groves2016TheSO,
  title={The structure of limit groups over hyperbolic groups},
  author={Daniel Groves and Henry Wilton},
  journal={Israel Journal of Mathematics},
  year={2016},
  volume={226},
  pages={119-176}
}
Let Γ be a torsion-free hyperbolic group. We study Γ-limit groups which, unlike the fundamental case in which Γ is free, may not be finitely presentable or geometrically tractable. We define model Γ-limit groups, which always have good geometric properties (in particular, they are always relatively hyperbolic). Given a strict resolution of an arbitrary Γ-limit group L, we canonically construct a strict resolution of a model Γ-limit group, which encodes all homomorphisms L → Γ that factor… 

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