Fourier Knots
Geometric Topology
2012-10-17 v1
Abstract
We show that every knot has a checkerbord diagram and that every knot is the closure of a rosette braid. We define Fourier knots of type (n_1, n_2, n_3) as knots which have parametrizations where each coordinate function x_i(t) is a finite Fourier series of length n_i, and conclude that every knot is a Fourier knot of type (1, 1, n) for some natural number n.
Keywords
Cite
@article{arxiv.1210.4543,
title = {Fourier Knots},
author = {Christoph Lamm},
journal= {arXiv preprint arXiv:1210.4543},
year = {2012}
}
Comments
This is a preprint from 1998 which became part of the first chapter of my Ph.D. thesis in 1999. The main result was later independently proven by Vassily Manturov (quasitoric braids). It should be cited as: Fourier Knots. Part of Ph.D. thesis 'Zylinder-Knoten und symmetrische Vereinigungen'. Bonner Mathematische Schriften 321 (1999)