Convergence group

Summary

In mathematics, a convergence group or a discrete convergence group is a group $\Gamma$ acting by homeomorphisms on a compact metrizable space $M$ in a way that generalizes the properties of the action of Kleinian group by Möbius transformations 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.