The lexicographic degree of the first two-bridge knots (1501.06393v2)

Published 23 Jan 2015 in math.GT and math.AG

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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