Reducible 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 (Tait 1898, Hoste et al. 1998) or removable crossings.

REFERENCES:

Hoste, J.; Thistlethwaite, M.; and Weeks, J. "The First  Knots." Math. Intell. 20, 33-48, Fall 1998.

Tait, P. G. "On Knots I, II, and III." Scientific Papers, Vol. 1. Cambridge, England: University Press, pp. 273-347, 1898.