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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


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.


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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.


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

Primary: 57M25
Secondary: 49Q10 , 53A04

Keywords: knots , links , quadrisecants , ropelength of knots , thickness of knots

Rights: Copyright © 2006 Mathematical Sciences Publishers

Vol.10 • No. 1 • 2006
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