Polygonal knot space near ropelength-minimized knots

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dc.creatorMillett, Kenneth C.
dc.creatorPiatek, Michael
dc.creatorRawdon, Eric J.
dc.date2005-08-16
dc.date.accessioned2026-07-07T05:22:24Z
dc.date.available2026-07-07T05:22:24Z
dc.descriptionFor a polygonal knot K, it is shown that a tube of radius R(K), the polygonal thickness radius, is an embedded torus. Given a thick configuration K, perturbations of size r<R(K) define satellite structures, or local knotting. We explore knotting within these tubes both theoretically and numerically. We provide bounds on perturbation radii for which we can see small trefoil and figure-eight summands and use Monte Carlo simulations to approximate the relative probabilities of these structures as a function of the number of edges.
dc.description33 pages, 25 figures
dc.identifierhttps://arxiv.org/abs/math/0508293
dc.identifierhttp://arxiv.org/abs/math/0508293
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76050
dc.subjectGeometric Topology
dc.subject57M25
dc.titlePolygonal knot space near ropelength-minimized knots
dc.typetext

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