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 S4 or RP4 or quotients of S3 × R by a cocompact fixed point free subgroup of the isometry group of the standard metric of S3 × R, or a connected sum of them. © 2012 J. Differential Geometry.