Complete classification of compact four-manifolds with positive isotropic curvature

Abstract

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 ${\mathbb{S}}^3\times \mathbb{R}$ by a cocompact fixed point free subgroup of the isometry group of the standard metric of ${\mathbb{S}}^3\times \mathbb{R}$, or a connected sum of them.

33 pages