Rational spheres and double disk bundles

Abstract

A manifold M is said to be a linear double disk bundle if it has two submanifolds B 1 and B 2 for which M is diffeomorphic to the normal bundles of the B i glued together along their common boundary. We show that if M n is a closed simply connected n-manifold with n even which is simultaneously a linear double disk bundle and a rational cohomology sphere, then M must be homeomorphic to a sphere.