Translator Disclaimer
2006 Quadrisecants give new lower bounds for the ropelength of a knot
Elizabeth Denne, Yuanan Diao, John M Sullivan
Geom. Topol. 10(1): 1-26 (2006). DOI: 10.2140/gt.2006.10.1

Abstract

Using the existence of a special quadrisecant line, we show the ropelength of any nontrivial knot is at least 15.66. This improves the previously known lower bound of 12. Numerical experiments have found a trefoil with ropelength less than 16.372, so our new bounds are quite sharp.

Citation

Download Citation

Elizabeth Denne. Yuanan Diao. John M Sullivan. "Quadrisecants give new lower bounds for the ropelength of a knot." Geom. Topol. 10 (1) 1 - 26, 2006. https://doi.org/10.2140/gt.2006.10.1

Information

Received: 27 September 2005; Revised: 27 December 2005; Accepted: 3 January 2006; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1108.57004
MathSciNet: MR2207788
Digital Object Identifier: 10.2140/gt.2006.10.1

Subjects:
Primary: 57M25
Secondary: 49Q10, 53A04

Rights: Copyright © 2006 Mathematical Sciences Publishers

JOURNAL ARTICLE
26 PAGES


SHARE
Vol.10 • No. 1 • 2006
MSP
Back to Top