The PIC1 open-manifold topology conjecture

Let $M$ be an open, complete, noncompact manifold without boundary whose curvature is PIC1. PIC1 open-manifold topology conjecture. $M$ is diffeomorphic to Euclidean space. This conjecture extends the Gromoll–Meyer theorem for positive sectional curvature and the Schoen–Yau theorem in dimension three. It is consistent with the fact that PIC1 and positive Ricci curvature coincide in three dimensions, and is known under a maximal volume-growth assumption, but remains open in general.