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

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

2009-12-16

arxiv.org/abs/0912.3282v1

Mathematics

Geometric Topology

53 pages, 28 figures

Scientific paper

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.

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