Hyperbolic Dehn filling, volume, and transcendentality
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908347627732992 |
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| author | Jeon, BoGwang Oh, Sunul |
| author_facet | Jeon, BoGwang Oh, Sunul |
| contents | Let $M$ be a 1-cusped hyperbolic 3-manifold. In this paper, we study the behavior of $N_M(v)$, the number of Dehn fillings of $M$ with a given volume $v(\in \mathbb{R})$. We conduct extensive computational experiments to estimate $N_M$ and propose a theoretical framework to explain its behavior. Further, we prove that the growth of $N_M$ is slower than any power of its filling coefficient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_11574 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hyperbolic Dehn filling, volume, and transcendentality Jeon, BoGwang Oh, Sunul Geometric Topology Number Theory 57K32, 57K31 Let $M$ be a 1-cusped hyperbolic 3-manifold. In this paper, we study the behavior of $N_M(v)$, the number of Dehn fillings of $M$ with a given volume $v(\in \mathbb{R})$. We conduct extensive computational experiments to estimate $N_M$ and propose a theoretical framework to explain its behavior. Further, we prove that the growth of $N_M$ is slower than any power of its filling coefficient. |
| title | Hyperbolic Dehn filling, volume, and transcendentality |
| topic | Geometric Topology Number Theory 57K32, 57K31 |
| url | https://arxiv.org/abs/2308.11574 |