Computing Chebyshev knot diagrams
Geometric Topology
2010-06-01 v2
Abstract
A Chebyshev curve C(a,b,c,\phi) has a parametrization of the form x(t)=Ta(t); y(t)=T_b(t) ; z(t)= Tc(t + \phi), where a,b,c are integers, Tn(t) is the Chebyshev polynomial of degree n and \phi \in \RR. When C(a,b,c,\phi) has no double points, it defines a polynomial knot. We determine all possible knots when a, b and c are given.
Keywords
Cite
@article{arxiv.1001.5192,
title = {Computing Chebyshev knot diagrams},
author = {Pierre-Vincent Koseleff and Daniel Pecker and Fabrice Rouillier},
journal= {arXiv preprint arXiv:1001.5192},
year = {2010}
}
Comments
8p