Geometry and topology of closed geodesics complements in the 3-torus
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913624453283840 |
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| author | Migueles, José Andrés Rodríguez |
| author_facet | Migueles, José Andrés Rodríguez |
| contents | We show that for at most three closed geodesics with linearly independent directions, the homeomorphism type of its complement in the 3-torus is determine by the orbit of their direction vectors subspaces under the action of $PSL_3(\mathbb{Z}).$ Moreover, we provide asymptotically sharp volume bounds for a family of closed geodesics complements. The bounds depend only on the distance in the Farey graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03838 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometry and topology of closed geodesics complements in the 3-torus Migueles, José Andrés Rodríguez Geometric Topology 57K32 (primary) 57K10, 57K35, 57Z15 (secondary) We show that for at most three closed geodesics with linearly independent directions, the homeomorphism type of its complement in the 3-torus is determine by the orbit of their direction vectors subspaces under the action of $PSL_3(\mathbb{Z}).$ Moreover, we provide asymptotically sharp volume bounds for a family of closed geodesics complements. The bounds depend only on the distance in the Farey graph. |
| title | Geometry and topology of closed geodesics complements in the 3-torus |
| topic | Geometric Topology 57K32 (primary) 57K10, 57K35, 57Z15 (secondary) |
| url | https://arxiv.org/abs/2412.03838 |