Self-contact Sets for 50 Tightly Knotted and Linked Tubes

Details Self-contact Sets for 50 Tightly Knotted and Linked Tubes Self-contact Sets for 50 Tightly Knotted and Linked Tubes

2005-08-15

arxiv.org/abs/math/0508248v1

Mathematics

Differential Geometry

26 pages, 53 figures, for higher-resolution images, see http://www.cs.washington.edu/homes/piatek/contact_table/

Scientific paper

We report on new numerical computations of the set of self-contacts in tightly knotted tubes of uniform circular cross-section. Such contact sets have been obtained before for the trefoil and figure eight knots by simulated annealing -- we use constrained gradient-descent to provide new self-contact sets for those and 48 other knot and link types. The minimum length of all unit diameter tubes in a given knot or link type is called the ropelength of that class of curves. Our computations yield improved upper bounds for the ropelength of all knots and links with 9 or fewer crossings except the trefoil.

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