  Both classical and virtual knots arise as formal Gauss diagrams modulo some
abstract moves corresponding to Reidemeister moves. If we forget about both
over/under crossings structure and writhe numbers of knots modulo the same
Reidemeister moves, we get a dramatic simplification of virtual knots, which
kills all classical knots. However, many virtual knots survive after this
simplification.
  We construct invariants of these objects and present their applications to
minimality problems of virtual knots as well as some questions related to
graph-links.
  One can easily generalize these results for the orientable case and apply
them for solving non-invertibility problems.
  The main idea behind these invariants is some geometrical construction which
reduces the general equivalence to the equivalence only modulo Reidemeister - 2
move.
