Modular knots obey the Chebotarev law
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866912170646700032 |
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| author | Ueki, Jun |
| author_facet | Ueki, Jun |
| contents | We study knots which behave like prime numbers. We discuss the planetary link raised from a hyperbolic fibered link in $S^3$ with an emphasis on surgeries, point out certain subtleness, and refine the construction. In addition, we point out a version of McMullen's theorem for the cases over cusped orbifolds and deduce that the family of modular knots around any torus knot $K_{a,b}$ in $S^3$ together with the missing knot $K_{a,b}$ obey the Chebotarev law. Furthermore, we attach several remarks in the view of arithmetic topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_10745 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Modular knots obey the Chebotarev law Ueki, Jun Geometric Topology Number Theory 37D99, 57K99, 57M99, 11N05 We study knots which behave like prime numbers. We discuss the planetary link raised from a hyperbolic fibered link in $S^3$ with an emphasis on surgeries, point out certain subtleness, and refine the construction. In addition, we point out a version of McMullen's theorem for the cases over cusped orbifolds and deduce that the family of modular knots around any torus knot $K_{a,b}$ in $S^3$ together with the missing knot $K_{a,b}$ obey the Chebotarev law. Furthermore, we attach several remarks in the view of arithmetic topology. |
| title | Modular knots obey the Chebotarev law |
| topic | Geometric Topology Number Theory 37D99, 57K99, 57M99, 11N05 |
| url | https://arxiv.org/abs/2105.10745 |