A knot with destabilized bridge spheres of arbitrarily high bridge number

Abstract

We show that there exists an infinite family of knots, each of which has, for each integer k>=0, a destabilized (2k+5)-bridge sphere. We also show that, for each integer n>=4, there exists a knot with a destabilized 3-bridge sphere and a destabilized n-bridge sphere.

20 pages, 17 figures, v2: minor corrections throughout the paper

References in corpus (4)

• Non-minimal bridge positions of torus knots are stabilized
• Flipping bridge surfaces and bounds on the stable bridge number
• A locally minimal, but not globally minimal bridge position of a knot
• Rectangle condition and its applications