Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 _\char93 }$ 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 _\char93 } = 0$ and $ {\partial _\char93 }\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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55P62, 55R05

Retrieve articles in all journals with MSC: 55P62, 55R05

Additional Information

Article copyright: © Copyright 1986 American Mathematical Society