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arXiv:0912.3282 [math.GT]AbstractReferencesReviewsResources

The Ropelengths of Knots Are Almost Linear in Terms of Their Crossing Numbers

Yuanan Diao, Claus Ernst, Attila Por, Uta Ziegler

Published 2009-12-16Version 1

For a knot or link K, let L(K) be the ropelength of K and Cr(K) be the crossing number of K. In this paper, we show that there exists a constant a>0 such that L(K) is bounded above by a Cr(K) ln^5 (Cr(K)) for any knot K. This result shows that the upper bound of the ropelength of any knot is almost linear in terms of its minimum crossing number.

Comments: 53 pages, 28 figures
Categories: math.GT
Subjects: 57M25
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