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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 rational homotopy type
of function spaces


Authors: Edgar H. Brown Jr. and Robert H. Szczarba Jr.
Journal: Trans. Amer. Math. Soc. 349 (1997), 4931-4951
MSC (1991): Primary 55P15, 55P62
MathSciNet review: 1407482
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Abstract: The main result of this paper is the construction of a minimal model for the function space $\mathcal {F}(X,Y)$ of continuous functions from a finite type, finite dimensional space $X$ to a finite type, nilpotent space $Y$ in terms of minimal models for $X$ and $Y$. For the component containing the constant map, $\pi _{*}(\mathcal {F}(X,Y))\otimes Q =\pi _{*}(Y)\otimes H^{-*}(X;Q)$ in positive dimensions. When $X$ is formal, there is a simple formula for the differential of the minimal model in terms of the differential of the minimal model for $Y$ and the coproduct of $H_{*}(X;Q)$. We also give a version of the main result for the space of cross sections of a fibration.


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Additional Information

Edgar H. Brown Jr.
Affiliation: Department of Mathematics, Brandeis University, Waltham, Massachusetts 02254

Robert H. Szczarba Jr.
Affiliation: Department of Mathematics, Yale University, Box 208283, New Haven, Connecticut 06520

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01871-0
PII: S 0002-9947(97)01871-0
Received by editor(s): February 12, 1996
Article copyright: © Copyright 1997 American Mathematical Society