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Complete classification of compact four-manifolds with positive isotropic curvature

Bing-Long Chen Sun Yat-Sen University Siu-Hung Tang Sun Yat-Sen University Xi-Ping Zhu Sun Yat-Sen University

Differential Geometry mathscidoc:1609.10264

Gold Award Paper in 2017

Journal of Differential Geometry, 91, (1), 41-80, 2012
In this paper, we completely classify all compact 4-manifolds with positive isotropic curvature. We show that they are diffeomorphic to S4 or RP4 or quotients of S3 ×R by a cocompact fixed point free subgroup of the isometry group of the standard metric of S3 × R, or a connected sum of them.
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@inproceedings{bing-long2012complete,
  title={COMPLETE CLASSIFICATION OF COMPACT FOUR-MANIFOLDS WITH POSITIVE ISOTROPIC CURVATURE},
  author={Bing-Long Chen, Siu-Hung Tang, and Xi-Ping Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913225501434983926},
  booktitle={Journal of Differential Geometry},
  volume={91},
  number={1},
  pages={41-80},
  year={2012},
}
Bing-Long Chen, Siu-Hung Tang, and Xi-Ping Zhu. COMPLETE CLASSIFICATION OF COMPACT FOUR-MANIFOLDS WITH POSITIVE ISOTROPIC CURVATURE. 2012. Vol. 91. In Journal of Differential Geometry. pp.41-80. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913225501434983926.
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