Upper Bounds for Ropelength as a Function of Crossing Number
arXiv:math/0210245 · doi:10.1016/S0166-8641(03)00168-8
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.
11 pages, 14 figures. Replacement corrects EPS font problem in figure