Lissajous knots and knots with Lissajous projections

Details Lissajous knots and knots with Lissajous projections Lissajous knots and knots with Lissajous projections

2006-05-24

arxiv.org/abs/math/0605632v1

Mathematics

Geometric Topology

17 pages, 11 figures

Scientific paper

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.

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