On the lexicographic degree of two-bridge knotsReport as inadecuate




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1 CMLS - Centre de Mathématiques Laurent Schwartz 2 UPMC - Université Pierre et Marie Curie - Paris 6 3 IMJ - Institut de Mathématiques de Jussieu 4 OURAGAN - OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs Inria Paris-Rocquencourt

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.

Keywords : polynomial knots Real pseudoholomorphic curves two-bridge knots





Author: Erwan Brugallé - Pierre-Vincent Koseleff - Daniel Pecker -

Source: https://hal.archives-ouvertes.fr/



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