Boundaries of Fuchsian groups (Ex)

A Fuchsian group $G$$<wikitex>; A Fuchsian group $G$ is a group which acts properly, co-compactly, and isometrically on the hyperbolic $-space $\mathbb{H}^2$. Show that $G$ is hyperbolic and describe its boundary. </wikitex> [[Category:Exercises]] [[Category:Exercises without solution]]G$ is a group which acts properly, co-compactly, and isometrically on the hyperbolic $2$$2$-space $\mathbb{H}^2$$\mathbb{H}^2$. Show that $G$$G$ is hyperbolic and describe its boundary.