Volume 10 (2006)
Download this article
For screen
For printing
Recent Issues

Volume 17 (2013)
Issue 1 1–620
Issue 2 621–

Volume 16 (2012) 1–4

Volume 15 (2011) 1–4

Volume 14 (2010) 1–5

Volume 13 (2009) 1–5

Volume 12 (2008) 1–5

Volume 11 (2007)

Volume 10 (2006)

Volume 9 (2005)

Volume 8 (2004)

Volume 7 (2003)

Volume 6 (2002)

Volume 5 (2001)

Volume 4 (2000)

Volume 3 (1999)

Volume 2 (1998)

Volume 1 (1997)

G&T Monographs
The Journal
About the Journal
Editorial Board
Editorial Interests
Author Index
Editorial procedure
Submission Guidelines
Submission Page
Author copyright form
Subscriptions
Contacts
G&T Publications
GTP Author Index

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

DOI: 10.2140/gt.2006.10.1

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

Primary: 57M25

Secondary: 49Q10, 53A04
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
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