# Chebotarev links are stably generic

## TL;DR

This paper explores the analogy between prime ideals in number fields and links in 3-manifolds, proving that sequences of knots following Chebotarev laws form stably generic links, with applications to hyperbolic links and knot decomposition phenomena.

## Contribution

It establishes that Chebotarev-law obeying knot sequences form stably generic links, connecting number theory and 3-manifold topology in a novel way.

## Key findings

- Sequences of knots obeying Chebotarev law form stably generic links.
- The planetary link of a fibered hyperbolic link exemplifies this phenomenon.
- A Chebotarev phenomenon is observed in a degree 5 non-Galois subcover of an A_5 cover.

## 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.