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arXiv:math/0408026 [math.GT]AbstractReferencesReviewsResources

Quadrisecants give new lower bounds for the ropelength of a knot

Elizabeth Denne, Yuanan Diao, John M Sullivan

Published 2004-08-02, updated 2009-02-09Version 3

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.

Comments: v3 is the version published by Geometry & Topology on 25 February 2006
Journal: Geom. Topol. 10 (2006) 1--26
Categories: math.GT, math.DG
Subjects: 57M25, 49Q10, 53A04
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