On possible existence of HOMFLY polynomials for virtual knots

Virtual knots are associated with knot diagrams, which are not obligatory planar. The recently suggested generalization from N=2N=2 to arbitrary N of the Kauffman–Khovanov calculus of cycles in resolved diagrams can be straightforwardly applied to non-planar case. In simple examples we demonstrate that this construction preserves topological invariance – thus implying the existence of HOMFLY extension of cabled Jones polynomials for virtual knots and links.