Geometric Simple connectivity in smooth Four-dimentional Topology (Po V-A): an outline

Abstract The main result of this paper is the following Theorem 1. Let 4 be a smooth compact bounded 4-manifold, which is geometrically simply-connected at long distance. It is assumed that @4 is a homology sphere. Then the open manifold int(4#1#(S2×D2)) is geometrically simply connected. The setting for this result is the diff category. Together with our earlier results it implies the Corollary 2. If 3 is a homotopy 3-ball then int((3×I)#1#(S2×D2)) is geometrically simply connected. This is one of the links which was missing in our program for the Poincaré Conjecture.