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Rational formality of mapping spaces

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Yves Félix

Let $X$ and $Y$ be finite nilpotent CW complexes with dimension of
$X$ less than the connectivity of $Y$. Generalizing results of
Vigu\'e-Poirrier and Yamaguchi, we prove that the mapping space
$\mbox{Map}(X,Y)$ is rationally formal if and only if $Y$ has the rational
homotopy type of a finite product of odd dimensional spheres.

Journal of Homotopy and Related Structures, Vol. 5(2010), No. 1, pp. 125-131