Scalar curvature, non-abelian group actions, and the degree of symmetry of exotic spheres

H Blaine Lawson Shing-Tung Yau

Differential Geometry mathscidoc:1912.43514

Commentarii Mathematici Helvetici, 49, (1), 232-244, 1974.12
It is proved that if a compact manifold admits a smooth action by a compact, connected, non-abelian Lie group, then it admits a metric of positive scalar curvature. This result is used to prove that if <sup> <i>n</i> </sup> is an exotic<i>n</i>-sphere which does not bound a spin manifold, then the only possible compact connected transformation groups of <sup> <i>n</i> </sup> are tori of dimension [(<i>n</i>+1)/2].
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@inproceedings{h1974scalar,
  title={Scalar curvature, non-abelian group actions, and the degree of symmetry of exotic spheres},
  author={H Blaine Lawson, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203733209529078},
  booktitle={Commentarii Mathematici Helvetici},
  volume={49},
  number={1},
  pages={232-244},
  year={1974},
}
H Blaine Lawson, and Shing-Tung Yau. Scalar curvature, non-abelian group actions, and the degree of symmetry of exotic spheres. 1974. Vol. 49. In Commentarii Mathematici Helvetici. pp.232-244. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203733209529078.
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