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

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 .

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 .

@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},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {31},
     number = {2},
     year = {1981},
     pages = {61-86},
     doi = {10.5802/aif.829},
     zbl = {0442.57009},
     mrnumber = {83a:57033},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1981__31_2_61_0}
}
Characteristic classes of subfoliations. Annales de l'Institut Fourier, Volume 31 (1981) no. 2, pp. 61-86. doi : 10.5802/aif.829. http://www.numdam.org/item/AIF_1981__31_2_61_0/

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