Vassiliev invariants of virtual framed and virtual Legendrian knots

We introduce virtual framed and virtual Legendrian knots. We then construct an isomorphism between the groups of Vassiliev invariants of virtual Legendrian knots and of virtual framed knots in the total space of the spherical cotangent bundle of a surface. This is philosophically related to the previous results of Fuchs–Tabachnikov, Goryunov, Hill and Chernov about isomorphisms of groups of Vassiliev invariants of (nonvirtual) Legendrian and topological knots.