Complete 4-manifolds with uniformly positive isotropic curvature

Abstract

We prove the following result: Let $(X,g_0)$ be a complete, connected 4-manifold with uniformly positive isotropic curvature and with bounded geometry. Then there is a finite collection $\mathcal{F}$ of manifolds of the form ${\mathbb{S}}^3\times \mathbb{R}/G$, where $G$ is a fixed point free discrete subgroup of the isometry group of the standard metric on ${\mathbb{S}}^3\times \mathbb{R}$, such that $X$ is diffeomorphic to a (possibly infinite) connected sum of copies of ${\mathbb{S}}^4,{\mathbb{RP}}^4$ and/or members of $\mathcal{F}$. This extends recent work of Chen-Tang-Zhu and Huang. We also extend the above result to the case of orbifolds. The proof uses Ricci flow with surgery on complete orbifolds.

The paper has been withdrawn by the author since it will be incorporated in the newest version of arXiv:1107.1469

References in corpus (2)

• Ricci flow with surgery on three-manifolds
• Ricci flow on open 3-manifolds and positive scalar curvature

Cited by in corpus (3)

• Ricci flow on open 3-manifolds and positive scalar curvature
• Three-orbifolds with positive scalar curvature
• Ricci flow on open 4-manifolds with positive isotropic curvature