2005/08/16 by Kenneth C. Millett, Millett, Kenneth C., Michael Piatek +3
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #Advanced Materials and Mechanics #Connective tissue disorders research #Geometric and Algebraic Topology #math.GT #msc:57M25
paper · pdf · doi:10.48550/arxiv.math/0508293
33 pages, 25 figures
arxiv created 2005/08/16 · arxiv updated 2009/12/01
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 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.