Alternating Quadrisecants of Knots
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2005
 arXiv:
 arXiv:math/0510561
 Bibcode:
 2005math.....10561D
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Differential Geometry;
 57M25
 EPrint:
 37 pages, 22 figures