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=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. 
Alexei Morozov, Andrey Morozov and Anton Morozov
hep-th math-ph math.GT math.MP