Vertex distortion of lattice knots
Publication Date
6-1-2021
Document Type
Article
Publication Title
Journal of Knot Theory and its Ramifications
Volume
30
Issue
7
DOI
10.1142/S0218216521500437
Abstract
The vertex distortion of a lattice knot is the supremum of the ratio of the distance between a pair of vertices along the knot and their distance in the ℓ1-norm. Inspired by Gromov, Pardon and Blair-Campisi-Taylor-Tomova, we show that results about the distortion of smooth knots hold for vertex distortion: the vertex distortion of a lattice knot is 1 only if it is the unknot, and there are minimal lattice-stick number knot conformations with arbitrarily high distortion.
Keywords
distortion, Lattice knots
Department
Mathematics and Statistics
Recommended Citation
Marion Campisi and Nicholas Cazet. "Vertex distortion of lattice knots" Journal of Knot Theory and its Ramifications (2021). https://doi.org/10.1142/S0218216521500437
