English

Chebotarev links are stably generic

Geometric Topology 2021-03-09 v5 Dynamical Systems Number Theory

Abstract

We discuss the relationship between two analogues in a 3-manifold of the set of prime ideals in a number field. We prove that if (Ki)iN>0(K_i)_{i\in \mathbb{N}_{>0}} is a sequence of knots obeying the Chebotarev law in the sense of Mazur and McMullen, then K=iKi\mathcal{K}=\cup_i K_i is a stably generic link in the sense of Mihara. An example we investigate is the planetary link of a fibered hyperbolic finite link in S3S^3. We also observe a Chebotarev phenomenon of knot decomposition in a degree 5 non-Galois subcover of an A5A_5(icosahedral)-cover.

Keywords

Cite

@article{arxiv.1902.06906,
  title  = {Chebotarev links are stably generic},
  author = {Jun Ueki},
  journal= {arXiv preprint arXiv:1902.06906},
  year   = {2021}
}

Comments

10 pages, several notes and Remark 10 are inserted in ver 2, the reference is refined in ver 3, several English errors are corrected and the title is changed in ver 4, "Corrigendum" is added in ver 5

R2 v1 2026-06-23T07:44:29.738Z