English

Quadrisecants give new lower bounds for the ropelength of a knot

Geometric Topology 2014-11-11 v3 Differential Geometry

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

Cite

@article{arxiv.math/0408026,
  title  = {Quadrisecants give new lower bounds for the ropelength of a knot},
  author = {Elizabeth Denne and Yuanan Diao and John M Sullivan},
  journal= {arXiv preprint arXiv:math/0408026},
  year   = {2014}
}

Comments

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