Compact group actions and maps into 𝐾(𝜋,1)-spaces

Gottlieb, Daniel H.; Lee, Kyung B.; Özaydin, Murad

doi:10.1090/S0002-9947-1985-0766228-2

Compact group actions and maps into $K(\pi ,1)$-spaces
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by Daniel H. Gottlieb, Kyung B. Lee and Murad Özaydin

Trans. Amer. Math. Soc. 287 (1985), 419-429

DOI: https://doi.org/10.1090/S0002-9947-1985-0766228-2

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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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