On torus knots and unknots (Q2809233)

This is a very nice paper on torus knots and unknots. Recall that a torus knot is a symmetric knot lying on a torus of revolution (with a circle as a section). The authors collect various results on such knots. In particular they show the existence of inflection points for a given critical aspect ratio, determine the location and prescribe the regularization condition to remove the local singularity associated with torsion, determine asymptotics of the topological crossing number, analyze several global geometric quantities (total curvature, writhing number, total torsion, and geometric ``energies'' given by total squared curvature and torsion, in relation to knot complexity measured by the winding number). The paper is concluded with application areas of torus knots.