Non-minimal bridge position of $2$-cable links

TL;DR

The paper proves that for certain cable links, any non-minimal bridge position can be simplified, extending a known property of knots to these links.

Contribution

It demonstrates that non-minimal bridge positions of (2, 2q)-cable links are perturbed if the same holds for the original knot, generalizing previous results.

Findings

Non-minimal bridge positions are perturbed for these links.

Extension of knot properties to cable links.

Supports simplification of complex link positions.

Abstract

Suppose that every non-minimal bridge position of a knot $K$ is perturbed. We show that if $L$ is a $(2, 2q)$-cable link of $K$, then every non-minimal bridge position of $L$ is also perturbed.