Dans ce travail on donne une construction des classes caractéristiques pour un sous-feuilletage , en suivant les méthodes de Kamber et Tondeur. Pour cela, on introduit la notion de fibré principal -feuilleté, et on définit un homomorphisme caractéristique qui lui est associé. On étudie la relation avec les homomorphismes caractéristiques des fibrés -feuilletés, et on calcule l’algèbre des classes caractéristiques en utilisant les résultats de Kamber et Tondeur sur la cohomologie de --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.
In this paper a construction of characteristic classes for a subfoliation is given by using Kamber-Tondeur’s techniques. For this purpose, the notion of -foliated principal bundle, and the definition of its associated characteristic homomorphism, are introduced. The relation with the characteristic homomorphism of -foliated bundles, , the results of Kamber-Tondeur on the cohomology of --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.
@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},
pages = {219--245},
publisher = {Institut Fourier},
address = {Grenoble},
volume = {34},
number = {3},
year = {1984},
doi = {10.5802/aif.984},
mrnumber = {86c:57024},
zbl = {0519.57022},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/aif.984/}
}
TY - JOUR AU - Carballés, José Manuel TI - Characteristic homomorphism for $(F_1,F_2)$-foliated bundles over subfoliated manifolds JO - Annales de l'Institut Fourier PY - 1984 SP - 219 EP - 245 VL - 34 IS - 3 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.984/ DO - 10.5802/aif.984 LA - en ID - AIF_1984__34_3_219_0 ER -
%0 Journal Article %A Carballés, José Manuel %T Characteristic homomorphism for $(F_1,F_2)$-foliated bundles over subfoliated manifolds %J Annales de l'Institut Fourier %D 1984 %P 219-245 %V 34 %N 3 %I Institut Fourier %C Grenoble %U http://archive.numdam.org/articles/10.5802/aif.984/ %R 10.5802/aif.984 %G en %F 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, Tome 34 (1984) no. 3, pp. 219-245. doi : 10.5802/aif.984. http://archive.numdam.org/articles/10.5802/aif.984/
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