Recognition and constructive membership for discrete subgroups of $\mathrm{SL}_2(\mathbb{R})$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912084105625600 |
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| author | Markowitz, Ari |
| author_facet | Markowitz, Ari |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18315 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Recognition and constructive membership for discrete subgroups of $\mathrm{SL}_2(\mathbb{R})$ Markowitz, Ari Group Theory 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. |
| title | Recognition and constructive membership for discrete subgroups of $\mathrm{SL}_2(\mathbb{R})$ |
| topic | Group Theory |
| url | https://arxiv.org/abs/2410.18315 |