Distortion and the bridge distance of knots

Distortion and the bridge distance of knots

We extend techniques due to Pardon to show that there is a lower bound on the distortion of a knot in R3 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 numbe...

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Veröffentlicht in:Journal of topology 2020-06, Vol.13 (2), p.669-682
Hauptverfasser: Blair, Ryan, Campisi, Marion, Taylor, Scott A., Tomova, Maggy
Format: Artikel
Sprache:eng
Schlagworte:
57M27 (primary)
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Zusammenfassung:We extend techniques due to Pardon to show that there is a lower bound on the distortion of a knot in R3 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.
ISSN:1753-8416
1753-8424
DOI:10.1112/topo.12139