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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Differentiable group actions on homotopy spheres. III. Invariant subspheres and smooth suspensions
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by Reinhard Schultz PDF
Trans. Amer. Math. Soc. 275 (1983), 729-750 Request permission

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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Additional Information
  • © Copyright 1983 American Mathematical Society
  • 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