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Fourier Knots

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arxiv 1210.4543 v1 pith:KJODFFOO submitted 2012-10-16 math.GT

Christoph Lamm This is my paper · ORCID
classification math.GT
keywords fourierknoteveryknotstypebraidcheckerbordclosure
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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.

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  1. Quasitoric representation of generalized braids

    math.GT 2024-11 conditional novelty 5.0 of 10

    Every oriented normal generalized link is the closure of a quasitoric normal generalized braid, and the quasitoric braids form a subgroup.

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