ABSTRACT
Virtual knot theory was proposed by Kauffman [Kau]. This theory arises from the theory of knots in thickened surfaces Sg× I, first studied by Kauffman, Jaeger, and Saleur, see [JKS]. Virtual knots (and links) appear by projecting knots and links in Sg to R
2 and hence, Sg ×R onto R 3. By projecting link diagrams (i.e., graphs
of valency four with overcrossing and undercrossing structures at vertices) in Sg onto R2, one obtains diagrams on the plane. Virtual crossings arise as artefacts of such projection, i.e., intersection points of images of arcs, non-intersecting in Sg and classical crossings appear just as projections of crossings.
