Complete 4-manifolds with uniformly positive isotropic curvature

Details Complete 4-manifolds with uniformly positive isotropic curvature Complete 4-manifolds with uniformly positive isotropic curvature

2009-12-30

arxiv.org/abs/0912.5405v9

Mathematics

Differential Geometry

22 pages, more details added. arXiv admin note: substantial text overlap with arXiv:1108.2918

Scientific paper

In this note 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. The proof uses Ricci flow with surgery on complete orbifolds.

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