On polynomial Torus Knots

Details On polynomial Torus Knots On polynomial Torus Knots

2006-10-22

arxiv.org/abs/math/0610663v2

Mathematics

Algebraic Geometry

11 p. accepted for publication in Journal of Knot Theory and Ramifications

Scientific paper

We show that no torus knot of type $(2,n)$, $n>3$ odd, can be obtained from a
polynomial embedding $t \mapsto (f(t), g(t), h(t))$ where
$(\deg(f),\deg(g))\leq (3,n+1) $. Eventually, we give explicit examples with
minimal lexicographic degree.

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