Rational fibrations homogeneous spaces with positive Euler characteristics and Jacobians

H. Shiga; M. Tezuka

Annales de l'institut Fourier (1987)

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

Abstract

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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 .

How to cite

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Shiga, 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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  15. [15] J.C. THOMAS, Quelques questions commentées sur la fibre d'Eilengerg-Moore d'une fibration de Serre, Publ. Lille, 3, no 6 (1981). 
  16. [16] H. SHIGA, Classifying maps and homogeneous spaces, (preprint). 
  17. [17] A. KONO, H. SHIGA and M. TEZUKA, A note on the cohomology of a fiber space whose fiber is a homogeneous space, (preprint). Zbl0696.55019
  18. [18] H. SHIGA and M. TEZUKA, Cohomology automorphisms of some Homogeneous spaces, to appear in Topology and its applications (Singapore conference volume). Zbl0623.57031

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