Title
Polygonal knot space near ropelength-minimized knots
Department/School
Mathematics
Date
5-1-2008
Document Type
Article
Keywords
Equilateral knots, polygonal knots, perturbation, thick knots, satellite knots, local knots, ropelength
Abstract
For 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 one can obtain small trefoil and figure-eight summands and use Monte Carlo simulations to estimate the relative probabilities of these structures as a function of the number of edges.
Volume
17
Issue
5
Published in
Journal of Knot Theory and Its Ramifications
Citation/Other Information
Millett, K.C., Piatek, M., & Rawdon, E.J. (2008). Polygonal knot space near ropelength–minimized knots, Journal of Knot Theory and Its Ramifications, 17(5). 601–631.