#### Volume 12, issue 3 (2012)

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A Jørgensen–Thurston theorem for homomorphisms

### Yi Liu

Algebraic & Geometric Topology 12 (2012) 1301–1311
##### Abstract

We provide a description of the structure of the set of homomorphisms from a finitely generated group to any torsion-free ($3$–dimensional) Kleinian group with uniformly bounded finite covolume. This is analogous to the Jørgensen–Thurston Theorem in hyperbolic geometry.

##### Keywords
hyperbolic geometry, limit group, Dehn extension
##### Mathematical Subject Classification 2010
Primary: 57M07
Secondary: 57M50, 20F65