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  "body": "\n## Summary\n\nIn 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.\n",
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