Handle decompositions of simply connected five-manifolds. III

Abstract

We prove the existence of exact handle decomposition of a simply connected smooth or piecewise linear (PL) five-manifold with a standard simply connected boundary of signature zero, the triviality of a five-dimensional h- cobordism with ends of such type, and the uniqueness up to diffeomorphism (PL-isomorphism) of a smooth (PL)h -cobordism between a given simply connected four-manifold and the corresponding standard manifold.