# Rational fibrations homogeneous spaces with positive Euler characteristics and Jacobians

Annales de l'institut Fourier (1987)

- Volume: 37, Issue: 1, page 81-106
- ISSN: 0373-0956

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topShiga, H., and Tezuka, M.. "Rational fibrations homogeneous spaces with positive Euler characteristics and Jacobians." Annales de l'institut Fourier 37.1 (1987): 81-106. <http://eudml.org/doc/74746>.

@article{Shiga1987,

abstract = {We show that an orientable fibration whose fiber has a homotopy type of homogeneous space $G/U$ with rank $G=~\{\rm rang\}~U$ 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 $G$.},

author = {Shiga, H., Tezuka, M.},

journal = {Annales de l'institut Fourier},

keywords = {fibration whose fiber has a homotopy type of homogeneous space; totally nonhomologous to zero; rational coefficients; Jacobian; Weyl group},

language = {eng},

number = {1},

pages = {81-106},

publisher = {Association des Annales de l'Institut Fourier},

title = {Rational fibrations homogeneous spaces with positive Euler characteristics and Jacobians},

url = {http://eudml.org/doc/74746},

volume = {37},

year = {1987},

}

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

PB - Association des Annales de l'Institut Fourier

VL - 37

IS - 1

SP - 81

EP - 106

AB - We show that an orientable fibration whose fiber has a homotopy type of homogeneous space $G/U$ with rank $G=~{\rm rang}~U$ 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 $G$.

LA - eng

KW - fibration whose fiber has a homotopy type of homogeneous space; totally nonhomologous to zero; rational coefficients; Jacobian; Weyl group

UR - http://eudml.org/doc/74746

ER -

## References

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