English

Vertex distortion of lattice knots

Geometric Topology 2021-12-28 v3

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. We show analogous results to those of Gromov, Pardon and Blair-Campisi-Taylor-Tomova 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 that there are minimal lattice-stick number knot conformations with arbitrarily high distortion.

Keywords

Cite

@article{arxiv.2009.03502,
  title  = {Vertex distortion of lattice knots},
  author = {Marion Campisi and Nicholas Cazet},
  journal= {arXiv preprint arXiv:2009.03502},
  year   = {2021}
}