Modular knots obey the Chebotarev law

Jun Ueki

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arXiv · 2105.10745

Modular knots obey the Chebotarev law

Jun Ueki

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Abstract

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.

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BibTeX RIS

Jun Ueki. 2021-05-22. Modular knots obey the Chebotarev law. https://arxiv.org/abs/2105.10745

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