English

Distortion and the bridge distance of knots

Geometric Topology 2020-03-25 v2

Abstract

We extend techniques due to Pardon to show that there is a lower bound on the distortion of a knot in R3\mathbb{R}^3 proportional to the minimum of the bridge distance and the bridge number of the knot. We also exhibit an infinite family of knots for which the minimum of the bridge distance and the bridge number is unbounded and Pardon's lower bound is constant.

Keywords

Cite

@article{arxiv.1705.08490,
  title  = {Distortion and the bridge distance of knots},
  author = {Ryan Blair and Marion Campisi and Scott A. Taylor and Maggy Tomova},
  journal= {arXiv preprint arXiv:1705.08490},
  year   = {2020}
}

Comments

19 pages, 5 figures. Version 2 incorporates significant improvements in exposition. The paper has been accepted by Journal of Topology