Hyperbolicity and Volume of Hyperbolic Bongles
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arXiv
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| Autores principales: | , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866929659632943104 |
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| author | Adams, Colin Gomez-Paz, Francisco Kang, Jiachen Krause, Lukas Li, Gregory Li, Reyna Marple, Chloe Tan, Ziwei |
| author_facet | Adams, Colin Gomez-Paz, Francisco Kang, Jiachen Krause, Lukas Li, Gregory Li, Reyna Marple, Chloe Tan, Ziwei |
| contents | We consider a simple but infinite class of staked links known as bongles. We provide necessary and sufficient conditions for these bongles to be hyperbolic. Then, we prove that all balanced hyperbolic $n$-bongles have the same volume and the corresponding volume is an upper bound on the volume of any hyperbolic $n$-bongle for $n$ even. Moreover, all hyperbolic $n$-bongles have volume strictly less than $5n(1.01494\dots)$. We also include explicit volume calculations for all hyperbolic 3-bongles through 6-bongles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02360 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hyperbolicity and Volume of Hyperbolic Bongles Adams, Colin Gomez-Paz, Francisco Kang, Jiachen Krause, Lukas Li, Gregory Li, Reyna Marple, Chloe Tan, Ziwei Geometric Topology 57K32, 57K10 We consider a simple but infinite class of staked links known as bongles. We provide necessary and sufficient conditions for these bongles to be hyperbolic. Then, we prove that all balanced hyperbolic $n$-bongles have the same volume and the corresponding volume is an upper bound on the volume of any hyperbolic $n$-bongle for $n$ even. Moreover, all hyperbolic $n$-bongles have volume strictly less than $5n(1.01494\dots)$. We also include explicit volume calculations for all hyperbolic 3-bongles through 6-bongles. |
| title | Hyperbolicity and Volume of Hyperbolic Bongles |
| topic | Geometric Topology 57K32, 57K10 |
| url | https://arxiv.org/abs/2501.02360 |