nugatory crossing | removable crossing

A crossing in a knot diagram for which there exists a circle in the projection plane meeting the diagram transversely at that crossing, but not meeting the diagram at any other point. Removable crossings can be removed by twisting, and so cannot occur in a knot diagram of minimal link crossing number. Reducible crossings are also called nugatory crossings or removable crossings.

alternating knot | knot diagram | reduced knot diagram