Evolution method and HOMFLY polynomials for virtual knots
  Following the suggestion of arXiv:1407.6319 to lift the knot polynomials for virtual knots and links from Jones to HOMFLY, we apply the evolution method to calculate them for an infinite series of twist-like virtual knots and antiparallel 2-strand links. Within this family one can check topological invariance and understand how differential hierarchy is modified in virtual case. This opens a way towards a definition of colored (not only cabled) knot polynomials, though problems still persist beyond the first symmetric representation. 
Ludmila Bishler, Alexei Morozov, Andrey Morozov and Anton Morozov
hep-th math-ph math.GT math.MP