---
tag: NZ6HANMCHR
kind: concept
name: Convergence group
sources:
  - wikipedia: en:52297304@r1288088671
    locator: Convergence group
    note: adopted
    mention: wikipedia://en/52297304
    sections: [Summary]
same_as:
  wikidata: Q28136116
  wikipedia: Convergence group
inventory: [VBZVMZDPXH]
---

## Summary

In mathematics, a **convergence group** or a **discrete convergence group** is a group $\Gamma$ acting by [[homeomorphisms|0QT00PB5G2]] on a [[compact|0QPHW703PV]] [[metrizable space|091GJ3FYD7]] $M$ in a way that generalizes the properties of the action of Kleinian group by [[Möbius transformations|0B346DDAM5]] on the ideal boundary $\mathbb S^2$ of the hyperbolic 3-space $\mathbb H^3$. The notion of a convergence group was introduced by Gehring and Martin (1987)  and has since found wide applications in geometric topology, quasiconformal analysis, and geometric group theory.