Geodesic
Quadrisecants give new lower bounds for the ropelength of a knot
Denne, Elizabeth1 ; Diao, Yuanan2 ; Sullivan, John M3
1 Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138, USA
2 Department of Mathematics, University of North Carolina, Charlotte, North Carolina 28223, USA
3 Institut für Mathematik, MA 3–2, Technische Universität Berlin, D–10623 Berlin, Germany
Geometry & topology, Tome 10 (2006) no. 1, pp. 1-26.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/gt.2006.10.1
Keywords: Knots, links, thickness of knots, ropelength of knots, quadrisecants

Denne, Elizabeth 1 ; Diao, Yuanan 2 ; Sullivan, John M 3

1 Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138, USA
2 Department of Mathematics, University of North Carolina, Charlotte, North Carolina 28223, USA
3 Institut für Mathematik, MA 3–2, Technische Universität Berlin, D–10623 Berlin, Germany 
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Denne, Elizabeth; Diao, Yuanan; Sullivan, John M. Quadrisecants give new lower bounds for the ropelength of a knot. Geometry & topology, Tome 10 (2006) no. 1, pp. 1-26. doi : 10.2140/gt.2006.10.1. http://geodesic.mathdoc.fr/articles/10.2140/gt.2006.10.1/

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