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May 2012 Complete Classification of Compact Four-Manifolds with Positive Isotropic Curvature
Bing-Long Chen, Siu-Hung Tang, Xi-Ping Zhu
J. Differential Geom. 91(1): 41-80 (May 2012). DOI: 10.4310/jdg/1343133700

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 $\mathbb{RP}^4$ 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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Bing-Long Chen. Siu-Hung Tang. Xi-Ping Zhu. "Complete Classification of Compact Four-Manifolds with Positive Isotropic Curvature." J. Differential Geom. 91 (1) 41 - 80, May 2012. https://doi.org/10.4310/jdg/1343133700

Information

Published: May 2012
First available in Project Euclid: 24 July 2012

zbMATH: 1257.53053
MathSciNet: MR2944961
Digital Object Identifier: 10.4310/jdg/1343133700

Rights: Copyright © 2012 Lehigh University

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Vol.91 • No. 1 • May 2012
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