Dissolving knot surgered 4-manifolds by classical cobordism arguments

Abstract

The purpose of this note is to show that classical cobordism arguments, which go back to the pioneering works of Mandelbaum and Moishezon, provide quick and unified proofs of any knot surgered compact simply-connected 4-manifold [Formula: see text] becoming diffeomorphic to [Formula: see text] after a single stabilization by connected summing with [Formula: see text] or [Formula: see text], and almost complete decomposability of [Formula: see text] for many almost completely decomposable [Formula: see text], such as the elliptic surfaces.