Distortion and the bridge distance of knots

Ryan Blair; Marion Campisi; Scott A. Taylor; Maggy Tomova

doi:10.1112/topo.12139

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arXiv · 1705.08490

Distortion and the bridge distance of knots

Ryan Blair·Marion Campisi·Scott A. Taylor·Maggy Tomova

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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.

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Ryan Blair, Marion Campisi, Scott A. Taylor, Maggy Tomova. 2019-12-06. Distortion and the bridge distance of knots. https://doi.org/10.1112/topo.12139

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