Deformation of cylinder knots
arXiv:1210.6639
Abstract
Knots parametrized in cylinder coordinates by t -> (st, 3 + cos(nt), cos(mt + ϕ)) share properties of Lissajous and billiard knots in a cylinder. We use these 'billiard knots in a flat solid torus' to study two topics: when is Z(s,n,m) equal to Z(s,m,n)? And: why are the determinants of certain Lissajous and billiard knots in a cylinder equal?
This is the fourth chapter of my Ph.D. thesis in 1999. It should be cited as: Deformation of cylinder knots. Fourth chapter of Ph.D. thesis 'Zylinder-Knoten und symmetrische Vereinigungen'. Bonner Mathematische Schriften 321 (1999). Version 2 has address information and a journal update for Daniel Pecker's article