Alternating Quadrisecants of Knots [article]

E. Denne
2005 arXiv   pre-print
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.
arXiv:math/0510561v1 fatcat:nynrcafpijg5jfwg2kdujzo6gq