Unperturbed weakly reducible non-minimal bridge positions

Abstract

A bridge position of a knot is said to be perturbed if there exists a cancelling pair of bridge disks. Motivated by the examples of knots admitting unperturbed, strongly irreducible, non-minimal bridge positions due to Jang-Kobayashi-Ozawa-Takao, we derive examples of unperturbed, weakly reducible, non-minimal bridge positions. Also, a bridge version of Gordon’s Conjecture is proposed: the connected sum of unperturbed bridge positions is unperturbed.