Let K be a knot in the product of a surface F with a line . K is called GLOBAL if its projection into F is transverse to some generic vector field on F without critical points of index +1. Global knots generalize closed braids in the solid torus . We construct specific knot invariants of finite type for global knots . These invariants can not be extracted from the Kontsevich integral for knots in a thickened surface . We conjecture that our invariants separate global knots in general and we prove the conjecture in a particular case .

Moreover we use our invariants in order to prove the non-invertibility of certain links in the 3-sphere without making any use of the knot group !