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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Foliation preserving Lie group actions and characteristic classes
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by Haruo Suzuki PDF
Proc. Amer. Math. Soc. 85 (1982), 633-637 Request permission


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.
  • Raoul Bott, Lectures on characteristic classes and foliations, Lectures on algebraic and differential topology (Second Latin American School in Math., Mexico City, 1971) Lecture Notes in Math., Vol. 279, Springer, Berlin, 1972, pp. 1–94. Notes by Lawrence Conlon, with two appendices by J. Stasheff. MR 0362335
  • Shiing Shen Chern, Geometry of characteristic classes, Proceedings of the Thirteenth Biennial Seminar of the Canadian Mathematical Congress (Dalhousie Univ., Halifax, N.S., 1971) Canad. Math. Congr., Montreal, Que., 1972, pp. 1–40. MR 0370613
  • Michael-Robert Herman, The Godbillion-Vey invariant of foliations by planes of $T^{3}$, Geometry and topology (Proc. III Latin Amer. School of Math., Inst. Mat. Pura Aplicada CNPq, Rio de Janeiro, 1976) Lecture Notes in Math., Vol. 597, Springer, Berlin, 1977, pp. 294–307. MR 0451261
  • Daniel Lehmann, Classes caractéristiques exotiques et ${\cal I}$-connexité des espaces de connexions, Ann. Inst. Fourier (Grenoble) 24 (1974), no. 3, xiv, 267–306 (French, with English summary). Avec une appendice par B. Callenaere et D. Lehmann. MR 362342
  • Connor Lazarov and Herbert Shulman, Obstructions to foliation preserving Lie group actions, Topology 18 (1979), no. 3, 255–256. MR 546795, DOI 10.1016/0040-9383(79)90008-9
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 85 (1982), 633-637
  • MSC: Primary 57R30; Secondary 57R20
  • DOI:
  • MathSciNet review: 660619