A sliceness criterion for odd free knots

The problem of concordance and cobordism of knots is a well- known classical problem in low-dimensional topology. The purpose of this paper is to show that for odd free knots, that is, free knots with all intersections odd, the question of whether the knot is slice (concordant to a trivial knot) can be answered effectively by analysing pairing of the chords in a knot diagram. Bibliography: 8 titles.