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

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Commentarii Mathematici Helvetici

Abstract

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 ∑n is an exoticn-sphere which does not bound a spin manifold, then the only possible compact connected transformation groups of ∑n are tori of dimension ≤[(n+1)/2].

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Authors and Affiliations

  1. Dept. of Mathematics, University of California, 94720, Berkeley, Calif., USA

    H. Blaine Lawson Jr. & Shing Tung Yau

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  1. H. Blaine Lawson Jr.
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  2. Shing Tung Yau
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Research partially supported by the Sloan Foundation and NSF Grant GP-34785X.

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Lawson, H.B., Yau, S.T. Scalar curvature, non-abelian group actions, and the degree of symmetry of exotic spheres. Commentarii Mathematici Helvetici 49, 232–244 (1974). https://doi.org/10.1007/BF02566731

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  • DOI: https://doi.org/10.1007/BF02566731

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