Figure 2.

Example of calculation of the nullification writhe (w_x) and the remaining writhe (w_y) of a knot. Successive crossings are nullified until the unknot is reached, while, at each step, the diagram is prevented from becoming disconnected. The open ends arising after elimination of crossings are spliced in such a way that directionality along the knot contour is maintained. Then, w_x is the sum of the signs of the nullified crossings, and w_y is the sum of the signs of the remaining crossings, with w_x + w_y = w, the topological writhe.