On the evaluation map

Author:
Aniceto Murillo

Journal:
Trans. Amer. Math. Soc. **339** (1993), 611-622

MSC:
Primary 55P62; Secondary 18G15

DOI:
https://doi.org/10.1090/S0002-9947-1993-1112376-1

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 -connected topological space, with finite-dimensional rational homotopy, has finite-dimensional rational cohomology if and only if it has nontrivial evaluation map. (ii) Let 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 is surjective in rational homotopy and the evaluation map of is nontrivial, then the evaluation map of the fibre is different from zero.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1993-1112376-1

Keywords:
Evaluation map,
rational homotopy,
Sullivan models,
elliptic spaces,
Partially supported by a DGICYT grant (PB88-0329)

Article copyright:
© Copyright 1993
American Mathematical Society