Throughout this paper, by a knotted surface (or, synonymously, 2-knot) will always be meant a smooth embedding in IR of a compact 2-manifold M (where M is smooth, not necessarily connected, and is not assigned an orientation.) 1 By isotopy of two such smoothly knotted surfaces in IR, will be meant smooth ambient isotopy. There is a beautiful combinatorial description of the isotopy-classes of s...
