On the Minimum Ropelength of Knots and Links

Details On the Minimum Ropelength of Knots and Links On the Minimum Ropelength of Knots and Links

2001-03-30

arxiv.org/abs/math/0103224v3

Mathematics

Geometric Topology

29 pages, 14 figures; New version has minor additions and corrections; new section on asymptotic growth of ropelength; several

Scientific paper

The ropelength of a knot is the quotient of its length and its thickness, the radius of the largest embedded normal tube around the knot. We prove existence and regularity for ropelength minimizers in any knot or link type; these are $C^{1,1}$ curves, but need not be smoother. We improve the lower bound for the ropelength of a nontrivial knot, and establish new ropelength bounds for small knots and links, including some which are sharp.

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