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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Rational fibrations, minimal models, and fibrings of homogeneous spaces

Author: Stephen Halperin
Journal: Trans. Amer. Math. Soc. 244 (1978), 199-224
MSC: Primary 55F20
MathSciNet review: 0515558
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Abstract: Sullivan's theory of minimal models is used to study a class of maps called rational fibrations, which contains most Serre fibrations.

It is shown that if the total space has finite rank and the fibre has finite dimensional cohomology, then both fibre and base have finite rank.

This is applied to prove that certain homogeneous spaces cannot be the total space of locally trivial bundles.

In addition two main theorems are proved which exhibit a close relation between the connecting homomorphism of the long exact homotopy sequence, and certain properties of the cohomology of fibre and base.

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Keywords: Rational fibration, minimal model, connecting homomorphism, spaces of finite rank, homogeneous space
Article copyright: © Copyright 1978 American Mathematical Society