LISSAJOUS KNOTS-Reference-Cited by-同舟云学术

LISSAJOUS KNOTS

Published:1994-06 Issue:02 Volume:03 Page:121-140
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

BOGLE M. G. V.¹,HEARST J. E.²,JONES V. F. R.³,STOILOV L.³

Affiliation:

1. Water Engineering & Modelling, 766 North Mentor, Pasadena, California 91104, USA

2. Department of Chemistry, University of California, Structural Biology Division, Lawrence Berkeley Laboratory, Berkeley, California 94720, USA

3. Department of Mathematics, University of California, Berkeley, California 94720, USA

Abstract

A Lissajous knot is defined to be one isotopic to a knot which admits a parametrization (for 0≤t≤2π) [Formula: see text] Motivation for considering Lissajous knots came originally from the study of DNA molecular configurations. We will show that a Lissajous knot necessarily has Kervaire invariant zero so that the trefoil, figure-8 and the (2,5) torus knot are not Lissajous. The knot 52 can be realized with nx = 2, ny = 3, nz = 7.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216594000095

Cited by 39 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Manipulating ultrafast even-order nonlinear chiral responses of L-tryptophan by polarization pulse shaping;Proceedings of the National Academy of Sciences;2024-05-31

2. Parametric formation control of multiple nanosatellites for cooperative observation of China Space Station;Astrodynamics;2024-02-08

3. An Introduction to KnotPlot;Lecture Notes in Mathematics;2024

4. Visualization of the Oscillatory Dynamics of an Island Power System;2023 Workshop on Energy Data Visualization (EnergyVis);2023-10-22

5. A lower bound on the average genus of a 2-bridge knot;Journal of Knot Theory and Its Ramifications;2023-08