---
tag: A8N42XEQZ2
kind: concept
name: Kleinian model
sources:
  - wikipedia: en:1589114@r1351989494
    locator: Kleinian model
    note: adopted
    mention: wikipedia://en/1589114
    sections: [Summary]
same_as:
  wikidata: Q6420316
  wikipedia: Kleinian model
inventory: [RPPVCSE9EZ]
---

## Summary

In mathematics, a **Kleinian model** is a model of a three-dimensional hyperbolic manifold *N* by the [[quotient space|0NQ1H2X495]] $\mathbb{H}^3 / \Gamma$ 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.