Note on the rational cohomology of the function space of based maps

Yasusuke KOTANI

In this paper, for a formal, path connected, finite-dimen\-sional \CW-complex $X$ of finite type and a $q$-connected space $Y$ of finite type with $q \ge \dim{X}$, we determine the necessary and sufficient condition for the rational cohomology algebra $H^*(\F_*(X,Y);\Q)$ of the function space $\F_*(X,Y)$ of based maps to be free.

Homology, Homotopy and Applications, Vol. 6(2004), No. 1, pp. 341-350

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