On the Volume Conjecture for hyperbolic Dehn-filled 3-manifolds along the twist knots
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913565563158528 |
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| author | Ge, Huabin Meng, Yunpeng Wang, Chuwen Yang, Yuxuan |
| author_facet | Ge, Huabin Meng, Yunpeng Wang, Chuwen Yang, Yuxuan |
| contents | For a twist knot $\mathcal{K}_{p'}$, let $M$ be the closed $3$-manifold obtained by doing $(p, q)$ Dehn-filling along $\mathcal{K}_{p'}$. In this article, we prove that Chen-Yang's volume conjecture holds for sufficiently large $|p| + |q|$ and $|p'|$ for $M$. In the proof, we construct a new ideal triangulation of the Whitehead link complement which is different from Thurston's triangulation. Our triangulation has led to some new discoveries regarding symmetry, including insights into ``sister manifolds'' as introduced by Hodgson, Meyerhoff, and Weeks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20489 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Volume Conjecture for hyperbolic Dehn-filled 3-manifolds along the twist knots Ge, Huabin Meng, Yunpeng Wang, Chuwen Yang, Yuxuan Geometric Topology For a twist knot $\mathcal{K}_{p'}$, let $M$ be the closed $3$-manifold obtained by doing $(p, q)$ Dehn-filling along $\mathcal{K}_{p'}$. In this article, we prove that Chen-Yang's volume conjecture holds for sufficiently large $|p| + |q|$ and $|p'|$ for $M$. In the proof, we construct a new ideal triangulation of the Whitehead link complement which is different from Thurston's triangulation. Our triangulation has led to some new discoveries regarding symmetry, including insights into ``sister manifolds'' as introduced by Hodgson, Meyerhoff, and Weeks. |
| title | On the Volume Conjecture for hyperbolic Dehn-filled 3-manifolds along the twist knots |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2410.20489 |