Virtual knot

Summary

A virtual knot is an equivalence class of knot diagrams that may have, besides ordinary crossings, virtual crossings that are not really there. Louis Kauffman introduced them as a generalization of classical knots. Geometrically, virtual knots are knots in thickened surfaces, taken up to a suitable stabilization. Classical knots form a part of virtual knot theory: two classical knots that are equivalent as virtual knots are equivalent as classical knots.