Recognition and constructive membership for discrete subgroups of $\mathrm{SL}_2(\mathbb{R})$

Ari Markowitz

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arXiv · 2410.18315

Recognition and constructive membership for discrete subgroups of $\mathrm{SL}_2(\mathbb{R})$

Ari Markowitz

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Abstract

We provide algorithms to decide whether a finitely generated subgroup of $\mathrm{SL}_2(\mathbb{R})$ is discrete, solve the constructive membership problem for finitely generated discrete subgroups of $\mathrm{SL}_2(\mathbb{R})$, and compute a fundamental domain for a finitely generated Fuchsian group. These algorithms have been implemented in Magma for groups defined over real algebraic number fields.

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Ari Markowitz. 2024-10-23. Recognition and constructive membership for discrete subgroups of $\mathrm{SL}_2(\mathbb{R})$. https://arxiv.org/abs/2410.18315

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