A LEFT-RIGHT CLASSIFICATION OF TOPOLOGICALLY CHIRAL KNOTS

A method for partitioning topologically chiral knots into mutually heterochiral classes has been developed, based on the principle that for such knots there exist no diagrams whose vertex-bicolored graphs are composed of equivalent black and white subgraphs. The method, which introduces the concept of writhe profiles, is successfully applied to alternating as well as non-alternating prime and composite knots, and works in cases where the Jones and Kauffman polynomials fail to recognize the knot's chirality. It is shown that writhe profiles are sensitive indicators of diagram similarity.