Alternating Quadrisecants of Knots
Geometric Topology
2007-05-23 v1 Differential Geometry
Abstract
It is known that for every knotted curve in space, there is a line intersecting it in four places, a quadrisecant. Comparing the order of the four points along the line and knot we can distinguish three types of quadrisecants; the alternating ones have the most relevance for the geometry of a knot. In this paper we prove that every (nontrivial tame) knot has an alternating quadrisecant. This result had applications to the total curvature, second hull and ropelength of knots.
Keywords
Cite
@article{arxiv.math/0510561,
title = {Alternating Quadrisecants of Knots},
author = {E. Denne},
journal= {arXiv preprint arXiv:math/0510561},
year = {2007}
}
Comments
37 pages, 22 figures