Quadrisecants give new lower bounds for the ropelength of a knot

Abstract

Using the existence of a special quadrisecant line, we show the ropelength of any nontrivial knot is at least 15.66. This improves the previously known lower bound of 12. Numerical experiments have found a trefoil with ropelength less than 16.372, so our new bounds are quite sharp.

v3 is the version published by Geometry & Topology on 25 February 2006

References in corpus (4)

• On the Minimum Ropelength of Knots and Links
• The Second Hull of a Knotted Curve
• Alternating Quadrisecants of Knots
• The Distortion of a Knotted Curve

Cited by in corpus (12)

• Knot Tightening By Constrained Gradient Descent
• Ropelength Criticality
• Alternating Quadrisecants of Knots
• The Shapes of Tight Composite Knots
• A principle for ideal torus knots
• Spontaneous knotting of a flexible fiber in chaotic flows
• New lower bound for the distortion of a knotted curve
• Dynamics of Embedded Curves by Doubly-Nonlocal Reaction-Diffusion Systems
• The Ropelength of Special Alternating Knots
• Counterexamples to the quadrisecant approximation conjecture
• The ropelength conjecture of alternating knots
• Braid Index Bounds Ropelength From Below