Geometry & Topology Volume 10, issue 1 (2006)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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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

Bibliography

1	R Budney, J Conant, K P Scannell, D Sinha, New perspectives on self-linking, Adv. Math. 191 (2005) 78 MR2102844
2	J Cantarella, J Fu, R Kusner, J M Sullivan, N C Wrinkle, Criticality for the Gehring link problem, arXiv:math.DG/0402212
3	J Cantarella, G Kuperberg, R B Kusner, J M Sullivan, The second hull of a knotted curve, Amer. J. Math. 125 (2003) 1335 MR2018663
4	J Cantarella, R B Kusner, J M Sullivan, On the minimum ropelength of knots and links, Invent. Math. 150 (2002) 257 MR1933586
5	E Denne, Alternating quadrisecants of knots, PhD thesis, University of Illinois at Urbana–Champaign (2004) arXiv:math.GT/0510561
6	E Denne, J M Sullivan, The distortion of a knotted curve, arXiv:math.GT/0409438
7	E Denne, J M Sullivan, Convergence and isotopy for graphs of finite total curvature, preprint (2006)
8	Y Diao, The lower bounds of the lengths of thick knots, J. Knot Theory Ramifications 12 (2003) 1 MR1953620
9	A Dumitrescu, A Ebbers-Baumann, A Grüne, R Klein, G Rote, On the geometric dilation of closed curves, graphs and point sets, arXiv:math.MG/0407135
10	A Ebbers-Baumann, A Grüne, R Klein, Geometric dilation of closed planar curves: a new lower bound, from: "Proceedings of the 20th European Workshop on Computational Geometry (Seville 2004)"123
11	O Gonzalez, J H Maddocks, Global curvature, thickness, and the ideal shapes of knots, Proc. Natl. Acad. Sci. USA 96 (1999) 4769 MR1692638
12	L H Kauffman, Invariants of graphs in three-space, Trans. Amer. Math. Soc. 311 (1989) 697 MR946218
13	G Kuperberg, Quadrisecants of knots and links, J. Knot Theory Ramifications 3 (1994) 41 MR1265452
14	R B Kusner, J M Sullivan, On distortion and thickness of knots, from: "Topology and geometry in polymer science (Minneapolis, MN, 1996)", IMA Vol. Math. Appl. 103, Springer (1998) 67 MR1655037
15	H R Morton, D M Q Mond, Closed curves with no quadrisecants, Topology 21 (1982) 235 MR649756
16	E Pannwitz, Eine elementargeometrische Eigenschaft von Verschlingungen und Knoten, Math. Ann. 108 (1933) 629 MR1512869
17	P Pierański, In search of ideal knots, from: "Ideal knots", Ser. Knots Everything 19, World Sci. Publishing (1998) 20 MR1702021
18	E J Rawdon, Can computers discover ideal knots?, Experiment. Math. 12 (2003) 287 MR2034393
19	J M Sullivan, Approximating ropelength by energy functions, from: "Physical knots : knotting, linking, and folding geometric objects in ℝ³ (Las Vegas, NV, 2001)", Contemp. Math. 304, Amer. Math. Soc. (2002) 181 MR1953340