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Transactions of the American Mathematical Society

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

 

 

Free $ S\sp{1}$ actions and the group of diffeomorphisms


Author: Kai Wang
Journal: Trans. Amer. Math. Soc. 191 (1974), 113-127
MSC: Primary 57E15; Secondary 57D10
MathSciNet review: 0356106
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0356106-8
Keywords: Decomposable actions, splitting invariants, surgery, tangential homotopy complex projective spaces, characteristic spheres
Article copyright: © Copyright 1974 American Mathematical Society