Chebotarev links are stably generic

Jun Ueki

doi:10.1112/blms.12400

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arXiv · 1902.06906

Chebotarev links are stably generic

Jun Ueki

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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 $(K_i)_{i\in \mathbb{N}_{>0}}$ is a sequence of knots obeying the Chebotarev law in the sense of Mazur and McMullen, then $\mathcal{K}=\cup_i K_i$ 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 $S^3$. We also observe a Chebotarev phenomenon of knot decomposition in a degree 5 non-Galois subcover of an $A_5$(icosahedral)-cover.

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Jun Ueki. 2019-02-19. Chebotarev links are stably generic. https://doi.org/10.1112/blms.12400

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