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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Decomposition theorems in rational homotopy theory

Author: John Oprea
Journal: Proc. Amer. Math. Soc. 96 (1986), 505-512
MSC: Primary 55P62; Secondary 55R05
MathSciNet review: 822450
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Abstract: Let $F \to E \to B$ be a fibration of simply connected rational spaces with finite rational betti numbers. Denote the connecting homomorphism of the fibration by ${\partial _\# }$ and the Hurewicz map of the fibre $F$ by $h$. Then, it is shown that there is a decomposition $F \simeq \mathcal {F} \times K$ where $K$ is the product of rational Eilenberg-Mac Lane spaces contained in $\Omega B$ maximal with respect to the conditions: ${\pi _ * }\left ( K \right ) \cap \operatorname {Ker}{\partial _\# } = 0$ and ${\partial _\# }\left ( {{\pi _ * }\left ( K \right )} \right ) \cap \operatorname {Ker}h = 0$. This decomposition is obtained using Sullivan’s theory of minimal models. Applications are given of the main theorem and a dual result is proved for rational cofibrations.

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Article copyright: © Copyright 1986 American Mathematical Society