Quadrisecants give new lower bounds for the ropelength of a knot

Elizabeth Denne; Yuanan Diao; John M Sullivan

doi:10.2140/gt.2006.10.1

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Quadrisecants give new lower bounds for the ropelength of a knot

Elizabeth Denne·Yuanan Diao·John M Sullivan

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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.

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BibTeX RIS

Elizabeth Denne, Yuanan Diao, John M Sullivan. 2009-02-09. Quadrisecants give new lower bounds for the ropelength of a knot. https://doi.org/10.2140/gt.2006.10.1

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