The structure of limit groups over hyperbolic groups (with H. Wilton. Preprint (2016). .pdf

Abstract Let G be a torsion-free hyperbolic group. We study G-limit groups which, unlike the fundamental case in which G is free, may not be finitely presentable or geometrically tractable. We define model G-limit groups, which always have good geometric properties (in particular, they are always relatively hyperbolic). Given a strict resolution of an arbitrary G-limit group L, we canonicallly construct a strict resolution of a model G-limit group, which encodes all homomorphisms L --> G that factor through the given resolution. We propose this as the correct framework in which to study G-limit groups algorithmically. We enumerate all G-limit groups in this framework.