Four-orbifolds with 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 discrete subgroup of the isometry group of the round cylinder ${\mathbb{S}}^3\times \mathbb{R}$ on which $G$ acts freely, such that $X$ is diffeomorphic to a possibly infinite connected sum of ${\mathbb{S}}^4,{\mathbb{RP}}^4$ and 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.

slightly different from the published version

References in corpus (2)

• Geometrization of Three-Dimensional Orbifolds via Ricci Flow
• Three-orbifolds with positive scalar curvature

Cited by in corpus (1)

• Ricci flow on open 4-manifolds with positive isotropic curvature