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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The nonexistence of free $ S\sp{1}$ actions on some homotopy spheres


Author: Reinhard Schultz
Journal: Proc. Amer. Math. Soc. 27 (1971), 595-597
MSC: Primary 57.47
MathSciNet review: 0271985
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0271985-3
PII: S 0002-9939(1971)0271985-3
Keywords: Inertia group, exotic sphere, free differentiable action, PL and homotopy smoothings
Article copyright: © Copyright 1971 American Mathematical Society