2012/10/24 by Christoph Lamm, Lamm, Christoph
Computer Science · Mathematics · #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M25 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1210.6639
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
openalex publication_date 2012/10/24 · arxiv created 2012/11/20 · arxiv updated 2012/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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?