Characteristic homomorphism for (F 1 ,F 2 )-foliated bundles over subfoliated manifolds
Annales de l'Institut Fourier, Volume 34 (1984) no. 3, p. 219-245

In this paper a construction of characteristic classes for a subfoliation (F 1 ,F 2 ) is given by using Kamber-Tondeur’s techniques. For this purpose, the notion of (F 1 ,F 2 )-foliated principal bundle, and the definition of its associated characteristic homomorphism, are introduced. The relation with the characteristic homomorphism of F i -foliated bundles, i=1,2, the results of Kamber-Tondeur on the cohomology of g-DG-algebras. Finally, Goldman’s results on the restriction of foliated bundles to the leaves of a foliation are generalized, and the holonomy homomorphism of a leaf of a subfoliation is defined.

Dans ce travail on donne une construction des classes caractéristiques pour un sous-feuilletage (F 1 ,F 2 ), en suivant les méthodes de Kamber et Tondeur. Pour cela, on introduit la notion de fibré principal (F 1 ,F 2 )-feuilleté, et on définit un homomorphisme caractéristique qui lui est associé. On étudie la relation avec les homomorphismes caractéristiques des fibrés F i -feuilletés, i=1,2, et on calcule l’algèbre des classes caractéristiques en utilisant les résultats de Kamber et Tondeur sur la cohomologie de g-DG-algèbres. Finalement, on généralise les résultats de Goldman sur la restriction à une feuille d’un fibré feuilleté, et on définit l’homomorphisme d’holonomie d’une feuille d’un sous-feuilletage.

@article{AIF_1984__34_3_219_0,
     author = {Carball\'es, Jos\'e Manuel},
     title = {Characteristic homomorphism for $(F\_1,F\_2)$-foliated bundles over subfoliated manifolds},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {34},
     number = {3},
     year = {1984},
     pages = {219-245},
     doi = {10.5802/aif.984},
     zbl = {0519.57022},
     mrnumber = {86c:57024},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1984__34_3_219_0}
}
Carballés, José Manuel. Characteristic homomorphism for $(F_1,F_2)$-foliated bundles over subfoliated manifolds. Annales de l'Institut Fourier, Volume 34 (1984) no. 3, pp. 219-245. doi : 10.5802/aif.984. http://www.numdam.org/item/AIF_1984__34_3_219_0/

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