Computing fundamental domains for Fuchsian groups

TL;DR

This paper presents an algorithm to compute fundamental domains for cofinite Fuchsian groups, enabling the calculation of group invariants and explicit finite presentations.

Contribution

It introduces a novel algorithm for computing Dirichlet domains and invariants of cofinite Fuchsian groups, advancing computational methods in hyperbolic geometry.

Findings

Algorithm successfully computes Dirichlet domains for cofinite Fuchsian groups

Enables explicit calculation of group invariants and presentations

Improves computational tools for hyperbolic surface analysis

Abstract

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