Free $S^{1}$ actions and the group of diffeomorphisms
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- by Kai Wang
- Trans. Amer. Math. Soc. 191 (1974), 113-127
- DOI: https://doi.org/10.1090/S0002-9947-1974-0356106-8
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Abstract:
Let ${S^1}$ act linearly on ${S^{2p - 1}} \times {D^{2q}}$ and ${D^{2p}} \times {S^{2q - 1}}$ and let $f:{S^{2p - 1}} \times {S^{2q - 1}} \to {S^{2p - 1}} \times {S^{2q - 1}}$ be an equivariant diffeomorphism. Then there is a well-defined ${S^1}$ action on ${S^{2p - 1}} \times {D^{2q}}{ \cup _f}{D^{2p}} \times {S^{2q - 1}}$. An ${S^1}$ action on a homotopy sphere is decomposable if it can be obtained in this way. In this paper, we will apply surgery theory to study in detail the set of decomposable actions on homotopy spheres.References
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Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 191 (1974), 113-127
- MSC: Primary 57E15; Secondary 57D10
- DOI: https://doi.org/10.1090/S0002-9947-1974-0356106-8
- MathSciNet review: 0356106