Fundamental domains in $\mathrm{PSL}(2,\mathbb{R})$ for Fuchsian groups

Abstract

In this paper, we provide a necessary and sufficient condition for a set in $\mathrm{PSL}(2,\mathbb{R})$ or in $T^1{\mathbb{H}}^2$ to be a fundamental domain for a given Fuchsian group via its respective fundamental domain in the hyperbolic plane ${\mathbb{H}}^2$.

arXiv commentfinal version