The lexicographic degree of the first two-bridge knots

Erwan Brugallé; Pierre-Vincent Koseleff; Daniel Pecker

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arXiv · 1501.06393

The lexicographic degree of the first two-bridge knots

Erwan Brugallé·Pierre-Vincent Koseleff·Daniel Pecker

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Abstract

We study the degree of polynomial representations of knots. We give the lexicographic degree of all two-bridge knots with 11 or fewer crossings. First, we estimate the total degree of a lexicographic parametrisation of such a knot. This allows us to transform this problem into a study of real algebraic trigonal plane curves, and in particular to use the braid theoretical method developed by Orevkov.

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Erwan Brugallé, Pierre-Vincent Koseleff, Daniel Pecker. 2015-01-23. The lexicographic degree of the first two-bridge knots. https://arxiv.org/abs/1501.06393

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