Molecular design and tailor of the doubled knots

Abstract

A new method for understanding the relations between molecular design and topological features has been developed on the basis of the Seifert construction in knot theory. Our result shows that the T 2 k -molecular doubled knots possess the point symmetry group C 2 and that the T 2 k+1 -molecular doubled knots possess the point symmetry group C 1. Hence both sets are topological chiral. When the rungs are cut down, topological symmetries of the molecular knots are unchanged, except for the molecular knots 0 1 and 4 1. Moreover, the novel topology of the topological rubber glove has been discussed. Our results led us to infer that the point symmetry group S 1 is necessary and sufficient for the molecular topological rubber glove.