Hyperbolic Handlebody Complements in 3-Manifolds
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915131587297280 |
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| author | Adams, Colin Gomez-Paz, Francisco Kang, Jiachen Krause, Lukas Li, Gregory Marple, Chloe Tan, Ziwei |
| author_facet | Adams, Colin Gomez-Paz, Francisco Kang, Jiachen Krause, Lukas Li, Gregory Marple, Chloe Tan, Ziwei |
| contents | Let $M_0$ be a compact and orientable 3-manifold. After capping off spherical boundaries with balls and removing any torus boundaries, we prove that the resulting manifold $M$ contains handlebodies of arbitrary genus such that the closure of their complement is hyperbolic. We then extend the octahedral decomposition to obtain bounds on volume for some of these handlebody complements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_19330 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hyperbolic Handlebody Complements in 3-Manifolds Adams, Colin Gomez-Paz, Francisco Kang, Jiachen Krause, Lukas Li, Gregory Marple, Chloe Tan, Ziwei Geometric Topology 57K32 Let $M_0$ be a compact and orientable 3-manifold. After capping off spherical boundaries with balls and removing any torus boundaries, we prove that the resulting manifold $M$ contains handlebodies of arbitrary genus such that the closure of their complement is hyperbolic. We then extend the octahedral decomposition to obtain bounds on volume for some of these handlebody complements. |
| title | Hyperbolic Handlebody Complements in 3-Manifolds |
| topic | Geometric Topology 57K32 |
| url | https://arxiv.org/abs/2501.19330 |