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Journal Articles Journal of Knot Theory and Its Ramifications Year : 2016

On the lexicographic degree of two-bridge knots

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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Dates and versions

hal-01084472 , version 1 (19-11-2014)
hal-01084472 , version 2 (23-11-2014)

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Erwan Brugallé, Pierre-Vincent Koseleff, Daniel Pecker. On the lexicographic degree of two-bridge knots. Journal of Knot Theory and Its Ramifications, 2016, 25 (7), ⟨10.1142/S0218216516500449⟩. ⟨hal-01084472v2⟩
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