We show that an orientable fibration whose fiber has a homotopy type of homogeneous space with rank is totally non homologous to zero for rational coefficients. The Jacobian formed by invariant polynomial under the Weyl group of plays a key role in the proof. We also show that it is valid for mod. coefficients if does not divide the order of the Weyl group of .
Nous démontrons que la fibration orientable de fibre ayant même type d’homotopie que l’espace homogène avec rang est totalement non homologue à zéro pour les coefficients rationnels. Nous utilisons le jacobien formé par des poloynômes invariants pour le groupe de Weyl de . Nous démontrons également que le résultat est valable pour les coefficients mod. si ne divise pas l’ordre du groupe de Weyl de .
@article{AIF_1987__37_1_81_0, author = {Shiga, H. and Tezuka, M.}, title = {Rational fibrations homogeneous spaces with positive {Euler} characteristics and {Jacobians}}, journal = {Annales de l'Institut Fourier}, pages = {81--106}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {37}, number = {1}, year = {1987}, doi = {10.5802/aif.1078}, mrnumber = {89g:55019}, zbl = {0608.55006}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1078/} }
TY - JOUR AU - Shiga, H. AU - Tezuka, M. TI - Rational fibrations homogeneous spaces with positive Euler characteristics and Jacobians JO - Annales de l'Institut Fourier PY - 1987 SP - 81 EP - 106 VL - 37 IS - 1 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1078/ DO - 10.5802/aif.1078 LA - en ID - AIF_1987__37_1_81_0 ER -
%0 Journal Article %A Shiga, H. %A Tezuka, M. %T Rational fibrations homogeneous spaces with positive Euler characteristics and Jacobians %J Annales de l'Institut Fourier %D 1987 %P 81-106 %V 37 %N 1 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.1078/ %R 10.5802/aif.1078 %G en %F AIF_1987__37_1_81_0
Shiga, H.; Tezuka, M. Rational fibrations homogeneous spaces with positive Euler characteristics and Jacobians. Annales de l'Institut Fourier, Volume 37 (1987) no. 1, pp. 81-106. doi : 10.5802/aif.1078. http://www.numdam.org/articles/10.5802/aif.1078/
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