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Transactions of the American Mathematical Society

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

 

 

Rational fibrations in differential homological algebra


Author: Aniceto Murillo
Journal: Trans. Amer. Math. Soc. 332 (1992), 79-91
MSC: Primary 55P62; Secondary 18G15
DOI: https://doi.org/10.1090/S0002-9947-1992-1079055-X
MathSciNet review: 1079055
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Abstract: In this paper, a result of [6] is generalized as follows: Given a fibration $ F \to E\xrightarrow{p}B$ of simply connected spaces in which either, the fibre has finite dimensional rational cohomology, or, it has finite dimensional rational homotopy and $ \rho $ induces a surjection in rational homotopy, we construct an explicit isomorphism,

\begin{displaymath}\begin{array}{*{20}{c}} {\varphi :\operatorname{Ext}_{{C^\ast... ...(E;{\mathbf{Q}})}(Q,{C^\ast}(E;{\mathbf{Q}})).} \\ \end{array} \end{displaymath}

This is deduced from its "algebraic translation," a more general result in the environment of graded differential homological algebra.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1992-1079055-X
Keywords: Rational fibration, differential homological algebra, Sullivan models
Article copyright: © Copyright 1992 American Mathematical Society