Some arithmetic aspects of ortho-integral surfaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909842898157568 |
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| author | Doan, Nhat Minh Le, Khanh |
| author_facet | Doan, Nhat Minh Le, Khanh |
| contents | We investigate ortho-integral (OI) hyperbolic surfaces with totally geodesic boundaries, defined by the property that every orthogeodesic (i.e. a geodesic arc meeting the boundary perpendicularly at both endpoints) has an integer cosh-length. We prove that while only finitely many OI surfaces exist for any fixed topology, infinitely many commensurability classes arise as the topology varies. Moreover, we completely classify OI pants and OI one-holed tori, and show that their doubles are arithmetic surfaces of genus 2 derived from quaternion algebras over $\mathbb{Q}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09403 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some arithmetic aspects of ortho-integral surfaces Doan, Nhat Minh Le, Khanh Geometric Topology Number Theory 32G15, 11E20 We investigate ortho-integral (OI) hyperbolic surfaces with totally geodesic boundaries, defined by the property that every orthogeodesic (i.e. a geodesic arc meeting the boundary perpendicularly at both endpoints) has an integer cosh-length. We prove that while only finitely many OI surfaces exist for any fixed topology, infinitely many commensurability classes arise as the topology varies. Moreover, we completely classify OI pants and OI one-holed tori, and show that their doubles are arithmetic surfaces of genus 2 derived from quaternion algebras over $\mathbb{Q}$. |
| title | Some arithmetic aspects of ortho-integral surfaces |
| topic | Geometric Topology Number Theory 32G15, 11E20 |
| url | https://arxiv.org/abs/2504.09403 |