In recent years, a ramification of knot theory, the theory of virtual knots, has rapidly developed. This theory was proposed by Lotus Kauffman in 1996. The theory originates from the theory of knots in thickened surfaces S_g x I. Virtual knots (or, generally, virtual links) appear as follows. Let us project a link in a thickened surface to the base S_g and indicate the overcrossing-undercrossing structure at crossings. While projecting S_g to R~2, the diagrams are projected as well. Thus, we obtain planar diagrams. Virtual crossings appear as artifacts of the projection, i.e., intersection points of the arcs, which have no intersection in S_g. One should mention that we consider the projection of the knot in the general position and exclude those cases where more than two branches have an intersection at the same point; thus, all crossings are just simple transversal intersections of two arcs of the projected knot (link).
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机译：近年来，虚拟结理论的结理论分支迅速发展。此理论是由Lotus Kauffman在1996年提出的。该理论起源于增厚表面S_g x I中的打结理论。虚拟打结（或通常为虚拟链接）如下所示。让我们在加厚表面上投影到基础S_g的链接，并指出交叉处的交叉交叉-交叉交叉结构。在将S_g投影到R〜2时，也将投影这些图。因此，我们获得了平面图。虚拟交叉点显示为投影的伪像，即弧的交点，在S_g中没有交点。应当提到的是，我们考虑了总体位置上的结点投影，并排除了两个以上分支在同一点有交点的情况；因此，所有交叉点都是投影结（链接）的两个弧线的简单横向交叉点。
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