We provide a description of the structure of the set of homomorphisms from a finitely generated group to any torsion-free (–dimensional) Kleinian group with uniformly bounded finite covolume. This is analogous to the Jørgensen–Thurston Theorem in hyperbolic geometry.
Yi Liu. "A Jørgensen–Thurston theorem for homomorphisms." Algebr. Geom. Topol. 12 (3) 1301 - 1311, 2012. https://doi.org/10.2140/agt.2012.12.1301