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On fundamental domains of arithmetic Fuchsian groups

Authors:	Stefan Johansson

Institution:	Department of Mathematics, Chalmers University of Technology and Göteborg University, S-412 96 Göteborg, Sweden

Abstract:	Let be a totally real algebraic number field and ${\mathcal{O}}$ an order in a quaternion algebra ${\mathfrak{A}}$ over . Assume that the group ${\mathcal{O}^{1}}$ of units in ${\mathcal{O}}$ with reduced norm equal to is embedded into $PSL_{2}({\mathbb{R})}$ as an arithmetic Fuchsian group. It is shown how Ford's algorithm can be effectively applied in order to determine a fundamental domain of ${\mathcal{O}^{1}}$ as well as a complete system of generators of ${\mathcal{O}^{1}}$ .

Keywords:	Arithmetic Fuchsian groups quaternion orders fundamental domains

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