Volume 10, issue 1 (2006)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Quadrisecants give new lower bounds for the ropelength of a knot

Elizabeth Denne, Yuanan Diao and John M Sullivan

Geometry & Topology 10 (2006) 1–26

arXiv: math.GT/0408026

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.

Keywords
Knots, links, thickness of knots, ropelength of knots, quadrisecants
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 49Q10, 53A04
References
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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
Authors
Elizabeth Denne
Department of Mathematics
Harvard University
Cambridge
Massachusetts 02138
USA
Yuanan Diao
Department of Mathematics
University of North Carolina
Charlotte
North Carolina 28223
USA
John M Sullivan
Institut für Mathematik
MA 3–2
Technische Universität Berlin
D–10623 Berlin
Germany