2005/10/26 by Elizabeth Denne, E. Denne, Denne, E.
Computer Science · Engineering · Mathematics · #57M25 #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.DG #math.GT #msc:57M25
paper · pdf · doi:10.48550/arxiv.math/0510561
37 pages, 22 figures
arxiv created 2005/10/26 · openalex publication_date 2005/10/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.