Every knot is a billiard knot

Pierre-Vincent Koseleff (1, 2) , Daniel Pecker (2, 1)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 UPMC - Université Pierre et Marie Curie - Paris 6

We show that every knot can be realized as a billiard trajectory in a convex prism. This solves a conjecture of Jones and Przytycki.

Mots clés: Cylinder knots; Chebyshev knots; Billiard knots; Lissajous knots

Domaines: Géométrie algébrique [math.AG]; Topologie géométrique [math.GT]

Pierre-Vincent Koseleff, Daniel Pecker. Every knot is a billiard knot. Banach Center Publications, 2014, Knot in Poland III, 100 (1), pp.173-178. ⟨10.4064/bc100-0-9⟩. ⟨hal-00604080⟩