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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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