On the lexicographic degree of two-bridge knots

Erwan Brugallé; Pierre-Vincent Koseleff; Daniel Pecker

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arXiv · 1411.5793

On the lexicographic degree of 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 obtain the lexicographic degree for two-bridge torus knots and generalized twist knots. The proof uses the braid theoretical method developed by Orevkov to study real plane curves, combined with previous results from [KP10] and [BKP14]. We also give a sharp lower bound for the lexicographic degree of any knot, using real polynomial curves properties.

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Erwan Brugallé, Pierre-Vincent Koseleff, Daniel Pecker. 2014-11-24. On the lexicographic degree of two-bridge knots. https://arxiv.org/abs/1411.5793

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