Rational fibrations homogeneous spaces with positive Euler characteristics and Jacobians
Annales de l'Institut Fourier, Volume 37 (1987) no. 1, p. 81-106

We show that an orientable fibration whose fiber has a homotopy type of homogeneous space G/U with rank G= rang U is totally non homologous to zero for rational coefficients. The Jacobian formed by invariant polynomial under the Weyl group of G plays a key role in the proof. We also show that it is valid for mod.p coefficients if p does not divide the order of the Weyl group of G.

Nous démontrons que la fibration orientable de fibre ayant même type d’homotopie que l’espace homogène G/U avec rang G= rang U 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 G. Nous démontrons également que le résultat est valable pour les coefficients mod.p si p ne divise pas l’ordre du groupe de Weyl de G.

@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},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {37},
     number = {1},
     year = {1987},
     pages = {81-106},
     doi = {10.5802/aif.1078},
     mrnumber = {89g:55019},
     zbl = {0608.55006},
     language = {en},
     url = {aif.centre-mersenne.org/item/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. https://aif.centre-mersenne.org/item/AIF_1987__37_1_81_0/

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