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On the lexicographic degree of two-bridge knots

2014/11/21 by Erwan Brugallé, Pierre-Vincent Koseleff, Brugallé, Erwan +3
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #math.AG #math.GT

paper · pdf · doi:10.48550/arxiv.1411.5793

14p., 21 figs

arxiv created 2014/11/24 · arxiv updated 2014/11/25

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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