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Differential group actions on homotopy spheres. III. Invariant subspheres and smooth suspensions


Author: Reinhard Schultz
Journal: Trans. Amer. Math. Soc. 275 (1983), 729-750
MSC: Primary 57S15; Secondary 57R60, 57S17, 57S25
DOI: https://doi.org/10.1090/S0002-9947-1983-0682728-6
MathSciNet review: 682728
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Abstract: A linear action of an abelian group on a sphere generally contains a large family of invariant linear subspheres. In this paper the problem of finding invariant subspheres for more general smooth actions on homotopy spheres is considered. Classification schemes for actions with invariant subspheres are obtained; these are formally parallel to the classifications discussed in the preceding paper of this series. The realizability of a given smooth action as an invariant codimension two subsphere is shown to depend only on the ambient differential structure and an isotopy invariant. Applications of these results to specific cases are given; for example, it is shown that every exotic $ 10$-sphere admits a smooth circle action.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0682728-6
Article copyright: © Copyright 1983 American Mathematical Society

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