Upper bounds for ropelength as a function of crossing number

AbstractThis paper provides bounds for the ropelength of a link in terms of the crossing numbers of its prime 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