Complete classification of compact four-manifolds with positive isotropic curvature

In this paper, we completely classify all compact 4-manifolds with positive isotropic curvature. We show that they are diffeomorphic to $mathbb{S}^4,$ or $mathbb{R}mathbb{P}^4$ or quotients of $mathbb{S}^3times mathbb{R}$ by a cocompact fixed point free subgroup of the isometry group of the standard metric of $mathbb{S}^3times mathbb{R}$, or a connected sum of them.