Geometry & Topology 10 (2006) 1–26

DOI: 10.2140/gt.2006.10.1

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.

Keywords

Knots, links, thickness of knots, ropelength of knots, quadrisecants

Mathematical Subject Classification

Primary: 57M25

Secondary: 49Q10, 53A04

Publication

Received: 27 September 2005
Revised: 27 December 2005
Accepted: 3 January 2006
Published: 25 February 2006
Proposed: Joan Birman
Seconded: Dave Gabai, Walter Neumann

References

Authors