Grove's Double Soul Conjecture

Let $M$ be a closed simply connected smooth manifold admitting a Riemannian metric of non-negative sectional curvature. A double disk bundle is a smooth closed manifold obtained by gluing the total spaces of two disk bundles along their common boundary. Grove's Double Soul Conjecture. Then $M$ is a double disk bundle. This conjecture concerns the structure of closed simply connected non-negatively curved manifolds. The paper studies a generalization without simple connectivity and gives counterexamples to that generalized statement; the original conjecture is not resolved in the supplied text.