Alternating Quadrisecants of Knots

Details Alternating Quadrisecants of Knots Alternating Quadrisecants of Knots

2005-10-26

arxiv.org/abs/math/0510561v1

Mathematics

Geometric Topology

37 pages, 22 figures

Scientific paper

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.

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