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 [Formula: see text] of a knot [Formula: see text] is the infimum of the quotient of the length by the width among the ribbons representing a knot type of [Formula: see text]. This quantity tells how efficiently the folded ribbon is realized. Kusner conjectured that folded ribbonlength is bounded above by a linear function of the minimal crossing number [Formula: see text]. In this paper, we confirm that the folded ribbonlength of a 2-bridge knot [Formula: see text] is bounded above by [Formula: see text].