# Kleinian model

In mathematics, a Kleinian model is a model of a three-dimensional hyperbolic manifold N by the quotient space ${\displaystyle \mathbb {H} ^{3}/\Gamma }$ 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 ${\displaystyle \pi _{1}(N)}$ of the surface N. Many authors use the terms Kleinian group and Kleinian model interchangeably, letting one stand for the other.