Kleinian model

Summary

In mathematics, a Kleinian model is a model of a three-dimensional hyperbolic manifold N by the quotient space $\mathbb{H}^3 / \Gamma$ where $\Gamma$ is a discrete subgroup of PSL(2,C). Here, the subgroup $\Gamma$, a Kleinian group, is defined so that it is isomorphic to the fundamental group $\pi_1(N)$ of the surface N. Many authors use the terms Kleinian group and Kleinian model interchangeably, letting one stand for the other. The concept is named after Felix Klein.