Free differentiable actions of 𝑆¹ and 𝑆³ on homotopy spheres

Ku, Hsu-tung; Ku, Mei-chin

doi:10.1090/S0002-9939-1970-0264697-2

Free differentiable actions of $S^{1}$ and $S^{3}$ on homotopy spheres

Authors: Hsu-tung Ku and Mei-chin Ku
Journal: Proc. Amer. Math. Soc. 25 (1970), 864-869
MSC: Primary 57.47
DOI: https://doi.org/10.1090/S0002-9939-1970-0264697-2
MathSciNet review: 0264697
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Abstract: It is shown that there are homotopy $(4n + 1)$- or $(4n + 3)$-spheres which admit infinitely many differentiable free actions of ${S^1}$ or ${S^3}$ with characteristic homotopy spheres in certain dimensions and without characteristic homotopy spheres in some other dimensions.

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