Alternating Quadrisecants of Knots

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dc.creatorDenne, E.
dc.date2005-10-26
dc.date.accessioned2026-07-07T06:47:56Z
dc.date.available2026-07-07T06:47:56Z
dc.descriptionIt 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.
dc.description37 pages, 22 figures
dc.identifierhttps://arxiv.org/abs/math/0510561
dc.identifierhttp://arxiv.org/abs/math/0510561
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/103819
dc.subjectGeometric Topology
dc.subjectDifferential Geometry
dc.subject57M25
dc.titleAlternating Quadrisecants of Knots
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