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

H. Blaine Lawson; Shing Tung Yau

doi:10.1007/BF02566731

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

H. Blaine Lawson
, Shing Tung Yau

Mathematics

Stony Brook University

University of California at Berkeley

Research output: Contribution to journal › Article › peer-review

55 Scopus citations

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 exotic n-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].

Original language	English
Pages (from-to)	232-244
Number of pages	13
Journal	Commentarii Mathematici Helvetici
Volume	49
Issue number	1
DOIs	https://doi.org/10.1007/BF02566731
State	Published - Dec 1974

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

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

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