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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Foliation preserving Lie group actions and characteristic classes


Author: Haruo Suzuki
Journal: Proc. Amer. Math. Soc. 85 (1982), 633-637
MSC: Primary 57R30; Secondary 57R20
MathSciNet review: 660619
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Abstract: Let $ \tilde{\mathcal{F}}$ be a codimension $ k$ foliation of a manifold $ M$ and $ \mathcal{F}$ a subfoliation of $ \tilde{\mathcal{F}}$ with codimension $ q$. Let a Lie group $ G$ of dimension $ k$ act on $ M$ transversally locally freely to $ \tilde{\mathcal{F}}$ and preserving $ \mathcal{F}$. Let $ \mathcal{F}'$ be the foliation determined by $ \mathcal{F}$ and the $ G$-action. Then we have the following relations between exotic classes of $ \mathcal{F}$ and $ \mathcal{F}':{\alpha _\mathcal{F}}([{\hat c_I}{c_J}]) = {\alpha _{\mathcal{F}'}}([{\hat c_I}{c_J}])$ for $ I = ({i_1}, \ldots ,{i_\lambda })$, $ J = ({j_1}, \ldots ,{j_\mu })$, $ 1 \leqslant {j_\gamma },{j_l} \leqslant q - k$, and $ {\alpha _\mathcal{F}}([{\hat c_I}{c_J}]) = 0$ otherwise.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0660619-9
PII: S 0002-9939(1982)0660619-9
Keywords: Characteristic classes, foliations, Lie group actions
Article copyright: © Copyright 1982 American Mathematical Society