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Quadrisecants give new
lower bounds for the ropelength of a knot
Elizabeth Denne, Yuanan Diao and John M Sullivan |
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Geometry & Topology 10 (2006) 1–26
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DOI: 10.2140/gt.2006.10.1
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arXiv: math.GT/0408026 |
Abstract |
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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. |
Keywords
Knots, links, thickness of knots, ropelength of knots,
quadrisecants
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Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 49Q10, 53A04
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References |
Forward citations |
Publication
Received: 27 September 2005
Revised: 27 December 2005
Accepted: 3 January 2006
Published: 25 February 2006
Proposed: Joan Birman
Seconded: Dave Gabai, Walter Neumann
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Authors |
| Elizabeth Denne | |
| Department of Mathematics Harvard University Cambridge Massachusetts 02138 USA |
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| Yuanan Diao | |
| Department of Mathematics University of North Carolina Charlotte North Carolina 28223 USA |
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| John M Sullivan | |
| Institut für Mathematik MA 3–2 Technische Universität Berlin D–10623 Berlin Germany |
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