A locally minimal, but not globally minimal bridge position of a knot

Abstract

We give a locally minimal, but not globally minimal bridge position of a knot, that is, an unstabilized, nonminimal bridge position of a knot. It implies that a bridge position cannot always be simplified so that the bridge number monotonically decreases to the minimal.

27 pages, 12 figures, v3: minor corrections throughout the paper

References in corpus (3)

• Non-minimal bridge positions of torus knots are stabilized
• Flipping bridge surfaces and bounds on the stable bridge number
• Unexpected local minima in the width complexes for knots

Cited by in corpus (2)

• A knot with destabilized bridge spheres of arbitrarily high bridge number
• Uniqueness of higher genus bridge surfaces for torus knots