Unperturbed weakly reducible non-minimal bridge positions

TL;DR

This paper constructs examples of unperturbed weakly reducible non-minimal bridge positions of knots, and proposes a bridge version of Gordon's Conjecture relating to connected sums of such positions.

Contribution

It introduces new examples of unperturbed weakly reducible non-minimal bridge positions and formulates a bridge version of Gordon's Conjecture.

Findings

Examples of unperturbed weakly reducible non-minimal bridge positions are provided.

A bridge version of Gordon's Conjecture is proposed.

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.