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Rational fibrations homogeneous spaces with positive Euler characteristics and Jacobians

H. Shiga; M. Tezuka — 1987

Annales de l'institut Fourier

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 $G$ .

Cohomology of infinitesimal algebraic groups.

M. Kaneda; N. Shimada; M. Tezuka — 1990

Mathematische Zeitschrift

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