# Complete classification of compact four-manifolds with positive isotropic curvature

Research paper by Bing-Long Chen, Siu-Hung Tang, Xi-Ping Zhu

Indexed on: 11 Oct '08Published on: 11 Oct '08Published in: Mathematics - Differential Geometry

#### 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.