2002/10/16 by Jason Cantarella, Cantarella, Jason, X. W. Faber +3
Mathematics · #49Q10 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT #msc:49Q10
paper · pdf · doi:10.48550/arxiv.math/0210245
published as Topology Appl. 135 (2004) 253-264 · 11 pages, 14 figures. Replacement corrects EPS font problem in figure
arxiv created 2002/10/16 · arxiv updated 2026/08/03
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.