English

On polynomial Torus Knots

Algebraic Geometry 2011-11-09 v2

Abstract

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

Keywords

Cite

@article{arxiv.math/0610663,
  title  = {On polynomial Torus Knots},
  author = {Pierre-Vincent Koseleff and Daniel Pecker},
  journal= {arXiv preprint arXiv:math/0610663},
  year   = {2011}
}

Comments

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