GLUCK SURGERY AND FRAMED LINKS IN 4-MANIFOLDS

Gluck surgery is the operation of cutting out S² × D², a tubular neighborhood of a 2-knot and pasting it back in a 4-manifold. It may be expected to make a fake pair of 4-manifolds, which means a pair that are homotopy equivalent but non-diffeomorphic. We will give an alternative proof of a theorem: Gluck surgery along a banded 2-knot is independent of the bands, which was proved in P. Melvin's thesis and prove that: if a 2-knot is obtained by ribbon moves from another 2-knot, then the Gluck surgeries along them are diffeomorphic. Our method, which we call "framed links in 4-manifolds", is a (4,5)-dimensional version of the usual ((3,4)-dimensional) framed links.