Folded ribbonlength of 2-bridge knots

Abstract

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. 2020 Mathematics Subject Classification. 57K10. Key words and phrases. folded ribbonlength, folded ribbon knot, 2-bridge knot.