This paper is devoted to define a characteristic homomorphism for a subfoliation and to study its relation with the usual characteristic homomorphism for each foliation (as defined by Bott). Moreover, two applications are given: 1) the Yamato’s 2-codimensional foliation is shown to be no homotopic to in a (1,2)-codimensional subfoliation; 2) an obstruction to the existence of everywhere independent and transverse infinitesimal transformations of a foliation is obtained, when and these transformations generated a new foliation .
Le but de ce travail est de définir un homomorphisme caractéristique pour un sous-feuilletage et d’exposer la relation existante entre cet homomorphisme et l’homomorphisme caractéristique (à la Bott) pour chaque feuilletage. En plus, on donne deux applications : 1) on prouve que le feuilletage de Yamato en codimension 2 n’est pas homotopique à dans un sous-feuilletage de codimension (1,2); 2) on obtient une obstruction à l’existence de transformations infinitésimales d’un feuilletage qui soient partout indépendantes et transverses, et telles que et ces transformations engendrent un nouveau feuilletage .
@article{AIF_1981__31_2_61_0, author = {Cordero, Luis A. and Masa, X.}, title = {Characteristic classes of subfoliations}, journal = {Annales de l'Institut Fourier}, pages = {61--86}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {31}, number = {2}, year = {1981}, doi = {10.5802/aif.829}, zbl = {0442.57009}, mrnumber = {83a:57033}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.829/} }
TY - JOUR AU - Cordero, Luis A. AU - Masa, X. TI - Characteristic classes of subfoliations JO - Annales de l'Institut Fourier PY - 1981 SP - 61 EP - 86 VL - 31 IS - 2 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.829/ DO - 10.5802/aif.829 LA - en ID - AIF_1981__31_2_61_0 ER -
Cordero, Luis A.; Masa, X. Characteristic classes of subfoliations. Annales de l'Institut Fourier, Volume 31 (1981) no. 2, pp. 61-86. doi : 10.5802/aif.829. https://aif.centre-mersenne.org/articles/10.5802/aif.829/
[1] Lectures on characteristic classes and foliations, Lectures on Algebraic and Differential Topology, Lecture Notes in Math., vol. 279, Springer-Verlag, Berlin and New York, 1972, pp. 1-94. | MR | Zbl
,[2] On characteristic classes of Г-foliations, Bull. Amer. Math. Soc., 78 (1972), 1039-1044. | MR | Zbl
and ,[3] Exotic characteristic classes and subfoliations, Ann. Inst. Fourier, Grenoble, 26 (1976), 225-237; errata, ibid. 27, fasc. 4 (1977). | Numdam | MR | Zbl
and ,[4] Characteristic classes of flags of foliations. Functional Anal. Appl., 9 (1975), 312-317. | MR | Zbl
,[5] Cohomologies d'algèbres de Lie de champs de vecteurs, Séminaire Bourbaki, 25e année (1971/1972), n° 421. | Numdam | Zbl
,[6] Sur les classes caractéristiques des feuilletages, Séminaire Bourbaki, 24e année (1971/1972), n° 412. | Numdam | Zbl
,[7] Cohomology of Lie algebras, Ann. of Math., 57 (1953), 591-603. | MR | Zbl
and ,[8] Foliated bundles and characteristic classes, Lecture Notes in Math., vol. 493, Springer-Verlag, Berlin and New York, 1975. | MR | Zbl
and ,[9] Obstructions to foliation-preserving Lie group actions, Topology, 18 (1979), 255-256. | MR | Zbl
and ,[10] Obstructions to foliation-preserving vector fields, To appear in J. Pure and Appl. Algebra. | Zbl
and ,[11] Classes caractéristiques exotiques et J-connexité des espaces de connexions, Ann. Inst. Fourier, Grenoble, 24, 3 (1974), 267-306. | Numdam | MR | Zbl
,[12] Sur les classes exotiques des feuilletages. Géométrie Differentielle, Colloque, Santiago de Compostela, Espagne 1972, Lecture Notes in Math., vol. 392, Springer-Verlag, Berlin and New York, 1974, pp. 37-42. | MR | Zbl
,[13] A property of a characteristic class of an orbit foliation, Transform. Groups, Proc. Conf. Univ. Newcastle 1976, London Math. Soc. Lecture Notes Series, vol. 26 (1977), Cambridge Univ. Press, Cambridge, pp. 190-203. | MR | Zbl
,[14] Almost-multifoliate Riemannian manifolds, An. St. Univ. Iasi, 16 (1970), 97-103. | MR | Zbl
,[15] Examples of foliations with non-trivial exotic characteristic classes, Osaka J. Math., 12 (1975), 401-417. | MR | Zbl
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