  In the present paper, we construct a simple invariant which provides a
sliceness obstruction for {\em free knots}. This obstruction provides a new
point of view to the problem of studying cobordisms of curves immersed in
2-surfaces, a problem previously studied by Carter, Turaev, Orr, and others.
  The obstruction to sliceness is constructed by using the notion of {\em
parity} recently introduced by the author into the study of virtual knots and
their modifications. This invariant turns out to be an obstruction for
cobordisms of higher genera with some additional constraints.
