# Kleinian model

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In mathematics, a **Kleinian model** is a model of a three-dimensional hyperbolic manifold *N* by the quotient space where Γ is a discrete subgroup of PSL(2,**C**). Here, the subgroup Γ, a Kleinian group, is defined so that it is isomorphic to the fundamental group of the surface *N*. Many authors use the terms *Kleinian group* and *Kleinian model* interchangeably, letting one stand for the other.

Many properties of Kleinian models are in direct analogy to those of Fuchsian models; however, overall, the theory is less well developed. A number of unsolved conjectures on Kleinian models are the analogs to theorems on Fuchsian models.