Relationship Between Knots and Catenanes

The structure shown in magenta on the upper left is a 51 knot. The strand direction is indicated by the arrowheads appearing along the strand. When the two strands entering the lower node on the right exchange outgoing partners, the node disappears, and a 'zero node' is introduced. This converts the knot to a catenane shown in the upper right; the two linked cycles are drawn so as to retain their shapes, but they are drawn in different colors, cyan and red. The same catenane is redrawn on the lower left of the figure. The lower left node of the catenane undergoes a strand switch, and the structure is converted to a trefoil knot, illustrated on the lower right. Whereas the trefoil knot is a single strand, it is drawn with only a single color, magenta. Up

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