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