Complete classification of compact four-manifolds with positive isotropic curvature

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

2008-10-11

arxiv.org/abs/0810.1999v1

Mathematics

Differential Geometry

33 pages

Scientific paper

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.

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