Distortion and the bridge distance of knots

Abstract

We extend techniques due to Pardon to show that there is a lower bound on the distortion of a knot in ${\mathbb{R}}^3$ 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.

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

References in corpus (2)

• Bridge distance and plat projections
• Alternating links have representativity 2

Cited by in corpus (3)

• Vertex distortion of lattice knots
• Bridge indices of spatial graphs and diagram colorings
• Vertex distortion detects the unknot