2022/08/07 by Hyoung-Jun Kim, Kim, Hyoungjun, Sungjong No +3 · 3 citations
Engineering · Mathematics · Biochemistry, Genetics and Molecular Biology · #Advanced Materials and Mechanics #Geometric and Algebraic Topology #Microtubule and mitosis dynamics
paper · pdf · doi:10.48550/arxiv.2208.03669
A ribbon is a two-dimensional object with one-dimensional properties which is related with geometry, robotics and molecular biology. A folded ribbon structure provides a complex structure through a series of folds. We focus on a folded ribbon with knotted core. The folded ribbonlength Rib(K) of a knot K is the infimum of the quotient of length by width among the ribbons representing a knot type of K. This quantity tells how efficiently the folded ribbon is realized. Kusner conjectured that folded ribbonlength is bounded by a linear function of the minimal crossing number c(K). In this paper, we confirm that the folded ribbonlength of a 2-bridge knot K is bounded above by 2c(K)+2.