Lissajous knots and knots with Lissajous projections
Geometric Topology
2007-05-23 v1
Abstract
Knots in Euclidean space which may be parameterized by a single cosine function in each coordinate are called Lissajous knots. We show that twist knots are Lissajous knots if and only if their Arf invariants are zero. We further prove that all 2-bridge knots and all (3,q)-torus knots have Lissajous projections.
Cite
@article{arxiv.math/0605632,
title = {Lissajous knots and knots with Lissajous projections},
author = {Jim Hoste and Laura Zirbel},
journal= {arXiv preprint arXiv:math/0605632},
year = {2007}
}
Comments
17 pages, 11 figures