On the asymptotic expansions of various quantum invariants I: the colored Jones polynomial of twist knots at the root of unity $e^{\frac{2π\sqrt{-1}}{N+\frac{1}{2}}}$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866908406511566848 |
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| author | Chen, Qingtao Zhu, Shengmao |
| author_facet | Chen, Qingtao Zhu, Shengmao |
| contents | This is the first article in a series devoted to the study of the asymptotic expansions of various quantum invariants related to the twist knots. In this paper, by using the saddle point method developed by Ohtsuki, we obtain an asymptotic expansion formula for the colored Jones polynomial of twist knots $\mathcal{K}_p$ with $p\geq 6$ at the root of unity $e^{\frac{2π\sqrt{-1}}{N+\frac{1}{2}}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_12963 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the asymptotic expansions of various quantum invariants I: the colored Jones polynomial of twist knots at the root of unity $e^{\frac{2π\sqrt{-1}}{N+\frac{1}{2}}}$ Chen, Qingtao Zhu, Shengmao Geometric Topology Mathematical Physics Quantum Algebra This is the first article in a series devoted to the study of the asymptotic expansions of various quantum invariants related to the twist knots. In this paper, by using the saddle point method developed by Ohtsuki, we obtain an asymptotic expansion formula for the colored Jones polynomial of twist knots $\mathcal{K}_p$ with $p\geq 6$ at the root of unity $e^{\frac{2π\sqrt{-1}}{N+\frac{1}{2}}}$. |
| title | On the asymptotic expansions of various quantum invariants I: the colored Jones polynomial of twist knots at the root of unity $e^{\frac{2π\sqrt{-1}}{N+\frac{1}{2}}}$ |
| topic | Geometric Topology Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2307.12963 |