RIBBON KNOTS AND INVARIANTS OF THETA-CURVES

We define invariants of higher dimensional theta-curves, and give a characterization of a trivial curve in the case of the classical dimension. We introduce a ribbon presentation of a knot and equivalence in ribbon presentations. Then a ribbon presentation induces a theta-curve, and invariants of theta-curves give those of ribbon presentations. Using the invariants, we can distinguish ribbon presentations of a knot.