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.
"A Jørgensen–Thurston theorem for homomorphisms." Algebr. Geom. Topol. 12 (3) 1301 - 1311, 2012. https://doi.org/10.2140/agt.2012.12.1301