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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Differentiable pseudo-free circle actions on homotopy spheres


Author: Chao Chu Liang
Journal: Proc. Amer. Math. Soc. 72 (1978), 362-364
MSC: Primary 57S15; Secondary 57S25
DOI: https://doi.org/10.1090/S0002-9939-1978-0507339-8
MathSciNet review: 507339
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Abstract: Let G denote the circle group, $ \varphi $ a differentiable pseudo-free G-action of type $ ({p_1}, \ldots ,{p_k})$ on a homotopy sphere $ {\Sigma ^{2n + 1}}$, and X the vector field induced by $ \varphi $. If w is a G-invariant 1-form satisfying $ w(X) = 1$, then we will prove that $ {\smallint _\Sigma }w \wedge {(dw)^n} = \pm {({p_1}{p_2} \cdots {p_k})^{ - 1}}$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0507339-8
Keywords: Differentiable pseudo-free actions, V-manifolds, characteristic classes
Article copyright: © Copyright 1978 American Mathematical Society