Computing fundamental domains for Fuchsian groups

Voight, John

Journal de théorie des nombres de Bordeaux, Tome 21 (2009) no. 2, pp. 467-489.

Nous présentons un algorithme pour calculer un domaine de Dirichlet pour un groupe Fuchsien $\Gamma$, avec aire cofinie. Comme conséquence, nous calculons les invariants de $\Gamma$, ainsi qu’une présentation finie explicite pour $\Gamma$.

We exhibit an algorithm to compute a Dirichlet domain for a Fuchsian group $\Gamma$ with cofinite area. As a consequence, we compute the invariants of $\Gamma$, including an explicit finite presentation for $\Gamma$.

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