“…For the generalized moves one considers Reidemeister virtual moves consisting of Reidemeister classical moves and also virtual moves that can be regarded as versions of a single "bypass" move; more precisely, the branch of the knot containing only interior crossings can be removed and resurrected anywhere else in the plane (with the same endpoints). A more detailed description of the theory of virtual knots can be found in [5,15,20,21,26,36,37,38]. Virtual knots can also be interpreted topologically as knots in "thickened surfaces" S g ×I; the latter is the Cartesian product of a sphere with handles S g and the closed interval I, and the virtual knots are regarded to within isotopy and stabilization of these surfaces, that is, gluing and removal of new "thickened" handles which have empty intersection with the knot under consideration.…”