Nonminimal Bridge Position of 2-Cable Links

A knot (or link) in bridge position is said to be perturbed if there exists a cancelling pair of bridge disks, which gives rise to a lower index bridge position. For some classes of knots, every nonminimal bridge position is perturbed.We study whether such a property is preserved by cabling operation. In this paper, we show that the property is preserved for 2-cable links, that is, if every nonminimal bridge position of a knot K is perturbed, then every nonminimal bridge position of a 2-cable link L of K is also perturbed.