Rational fibrations, homogeneous spaces with positive Euler characteristics and Jacobians. (English) Zbl 0608.55006
We show that an orientable fibration whose fiber has homotopy type of a homogeneous space G/U with rank G\(=rank U\) is totally nonhomologous to zero for rational coefficients. The Jacobian formed by invariant polynomials 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.
MSC:
| 55R05 | Fiber spaces in algebraic topology |
| 55P62 | Rational homotopy theory |
| 53C30 | Differential geometry of homogeneous manifolds |
Keywords:
fibration whose fiber has a homotopy type of homogeneous space; totally nonhomologous to zero; rational coefficients; Jacobian; Weyl groupReferences:
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