Characteristic classes of subfoliations

Cordero, Luis A.; Masa, X.

Annales de l'Institut Fourier, Tome 31 (1981), p. 61-86 / Harvested from Numdam

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Résumé
Abstract

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 $F_{1}$ .

Publié le : 1981-01-01

MR 83a:57033 | Zbl 0442.57009 | 1 citation dans Numdam

DOI : https://doi.org/10.5802/aif.829

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     author = {Cordero, Luis A. and Masa, X.},
     title = {Characteristic classes of subfoliations},
     journal = {Annales de l'Institut Fourier},
     volume = {31},
     year = {1981},
     pages = {61-86},
     doi = {10.5802/aif.829},
     mrnumber = {83a:57033},
     zbl = {0442.57009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1981__31_2_61_0}
}

Cordero, Luis A.; Masa, X. Characteristic classes of subfoliations. Annales de l'Institut Fourier, Tome 31 (1981) pp. 61-86. doi : 10.5802/aif.829. http://gdmltest.u-ga.fr/item/AIF_1981__31_2_61_0/

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