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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Compact group actions and maps into $ K(\pi,1)$-spaces


Authors: Daniel H. Gottlieb, Kyung B. Lee and Murad Özaydin
Journal: Trans. Amer. Math. Soc. 287 (1985), 419-429
MSC: Primary 57S10; Secondary 55P20, 57S17
MathSciNet review: 766228
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Abstract: Let $ G$ act on an aspherical manifold $ M$. If $ G$ is a compact Lie group acting effectively and homotopically trivially then $ G$ must be abelian. We prove a much more general form of this result, thus extending results of Donnelly and Schultz. Our method gives us a splitting result for torus actions complementing a result of Conner and Raymond. We also generalize a theorem of Schoen and Yau on homotopy equivariance.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0766228-2
PII: S 0002-9947(1985)0766228-2
Keywords: Group actions on manifolds, $ K(\pi ,1)$-spaces, fundamental groups
Article copyright: © Copyright 1985 American Mathematical Society