Upper Bounds for Ropelength as a Function of Crossing Number
Geometric Topology
2007-05-23 v2 Differential Geometry
Abstract
The paper provides bounds for the ropelength of a link in terms of the crossing numbers of its split components. As in earlier papers, the bounds grow with the square of the crossing number; however, the constant involved is a substantial improvement on previous results. The proof depends essentially on writing links in terms of their arc-presentations, and has as a key ingredient Bae and Park's theorem that an n-crossing link has an arc-presentation with less than or equal to n+2 arcs.
Cite
@article{arxiv.math/0210245,
title = {Upper Bounds for Ropelength as a Function of Crossing Number},
author = {Jason Cantarella and X. W. Faber and Chad A. Mullikin},
journal= {arXiv preprint arXiv:math/0210245},
year = {2007}
}
Comments
11 pages, 14 figures. Replacement corrects EPS font problem in figure