Non-minimal bridge positions of torus knots are stabilized

Abstract

We show that any non-minimal bridge decomposition of a torus knot is stabilized and that $n$-bridge decompositions of a torus knot are unique for any integer $n$. This implies that a knot in a bridge position is a torus knot if and only if there exists a torus containing the knot such that it intersects the bridge sphere in two essential loops.

11 pages, 4 figures

Cited by in corpus (7)

• Unexpected local minima in the width complexes for knots
• Bridge spheres for the unknot are topologically minimal
• A locally minimal, but not globally minimal bridge position of a knot
• A knot with destabilized bridge spheres of arbitrarily high bridge number
• Bridge spectra of iterated torus knots
• Uniqueness of higher genus bridge surfaces for torus knots
• Goeritz groups of bridge decompositions