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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the evaluation map


Author: Aniceto Murillo
Journal: Trans. Amer. Math. Soc. 339 (1993), 611-622
MSC: Primary 55P62; Secondary 18G15
MathSciNet review: 1112376
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Abstract: The evaluation map of a differential graded algebra or of a space is described under two different approaches. This concept turns out to have geometric implications: (i) A $ 1$-connected topological space, with finite-dimensional rational homotopy, has finite-dimensional rational cohomology if and only if it has nontrivial evaluation map. (ii) Let $ E\xrightarrow{\rho }B$ be a fibration of simplyconnected spaces. If the rational cohomology of the fibre is finite dimensional and the evaluation map of the base is different from zero, then the evaluation map of the total space is nonzero. Also, if $ \rho $ is surjective in rational homotopy and the evaluation map of $ E$ is nontrivial, then the evaluation map of the fibre is different from zero.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1112376-1
PII: S 0002-9947(1993)1112376-1
Keywords: Evaluation map, rational homotopy, Sullivan models, elliptic spaces, Partially supported by a DGICYT grant (PB88-0329)
Article copyright: © Copyright 1993 American Mathematical Society