The nonexistence of free 𝑆¹ actions on some homotopy spheres

Schultz, Reinhard

doi:10.1090/S0002-9939-1971-0271985-3

The nonexistence of free $S^{1}$ actions on some homotopy spheres
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Proc. Amer. Math. Soc. 27 (1971), 595-597 Request permission

Abstract:

In this paper a necessary condition is given for the existence of a free differentiable action of the circle group ${S^1}$ on a $(4k + 1)$-dimensional homotopy sphere. This includes a previously known criterion due to R. Lee and yields additional examples of exotic spheres for which no such actions exist.

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