Global knot theory in F² x R

We introduce a special class of knots, called global knots, in F^2 x R and we construct new isotopy invariants, called T-invariants, for global knots. Some T-invariants are of finite type but they cannot be extracted from the generalized Kontsevitch integral (which is consequently not the universal invariant of finite type for the restricted class of global knots). We prove that T-invariants separate all global knots of a certain type. As a corollary, we prove the non-invertibility of some links in S^3 without making any use of the link group.