no. 2
Characteristic classes of subfoliations
Annales de l'Institut Fourier, Tome 31 (1981) no. 2, pp. 61-86.

Le but de ce travail est de définir un homomorphisme caractéristique pour un sous-feuilletage (F 1 ,F 2 ) 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 F 2 dans un sous-feuilletage de codimension (1,2); 2) on obtient une obstruction à l’existence de d transformations infinitésimales d’un feuilletage F 2 qui soient partout indépendantes et transverses, et telles que F 2 et ces transformations engendrent un nouveau feuilletage F 1 .

This paper is devoted to define a characteristic homomorphism for a subfoliation (F 1 ,F 2 ) 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 F 2 in a (1,2)-codimensional subfoliation; 2) an obstruction to the existence of d everywhere independent and transverse infinitesimal transformations of a foliation F 2 is obtained, when F 2 and these transformations generated a new foliation F 1 .

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Cordero, Luis A.; Masa, X. Characteristic classes of subfoliations. Annales de l'Institut Fourier, Tome 31 (1981) no. 2, pp. 61-86. doi : 10.5802/aif.829. https://aif.centre-mersenne.org/articles/10.5802/aif.829/

[1] R. Bott, 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] R. Bott and A. Haefliger, On characteristic classes of Г-foliations, Bull. Amer. Math. Soc., 78 (1972), 1039-1044. | MR | Zbl

[3] L. A. Cordero and P. M. Gadea, Exotic characteristic classes and subfoliations, Ann. Inst. Fourier, Grenoble, 26 (1976), 225-237; errata, ibid. 27, fasc. 4 (1977). | Numdam | MR | Zbl

[4] B. L. Feigin, Characteristic classes of flags of foliations. Functional Anal. Appl., 9 (1975), 312-317. | MR | Zbl

[5] C. Godbillon, Cohomologies d'algèbres de Lie de champs de vecteurs, Séminaire Bourbaki, 25e année (1971/1972), n° 421. | Numdam | Zbl

[6] A. Haefliger, Sur les classes caractéristiques des feuilletages, Séminaire Bourbaki, 24e année (1971/1972), n° 412. | Numdam | Zbl

[7] G. Hochschild and J. P. Serre, Cohomology of Lie algebras, Ann. of Math., 57 (1953), 591-603. | MR | Zbl

[8] F. Kamber and Ph. Tondeur, Foliated bundles and characteristic classes, Lecture Notes in Math., vol. 493, Springer-Verlag, Berlin and New York, 1975. | MR | Zbl

[9] C. Lazarov and H. Shulman, Obstructions to foliation-preserving Lie group actions, Topology, 18 (1979), 255-256. | MR | Zbl

[10] C. Lazarov and H. Shulman, Obstructions to foliation-preserving vector fields, To appear in J. Pure and Appl. Algebra. | Zbl

[11] D. Lehmann, Classes caractéristiques exotiques et J-connexité des espaces de connexions, Ann. Inst. Fourier, Grenoble, 24, 3 (1974), 267-306. | Numdam | MR | Zbl

[12] R. Moussu, 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] H. Suzuki, 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] I. Vaisman, Almost-multifoliate Riemannian manifolds, An. St. Univ. Iasi, 16 (1970), 97-103. | MR | Zbl

[15] K. Yamato, Examples of foliations with non-trivial exotic characteristic classes, Osaka J. Math., 12 (1975), 401-417. | MR | Zbl

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