Note on the rational cohomology of the function space of based maps (Q1770306)

Let \(\text{map}_*(X,Y)\) be the space of based maps from \(X\) to \(Y\). Assume that \(X\) is a \(\mathbb{Q}\)-formal path connected finite CW-complex and \(Y\) is a \(r\)-connected space with \(r\geq\dim X\). The author uses the Haefliger model for a space of maps [\textit{A. Haeflinger}, Trans Am. Math. Soc. 273, 609--620 (1982; Zbl 0508.55019)] in order to determine the necessary and sufficient conditions for the rational algebra \(H^*(\text{map}_*(X,Y); \mathbb{Q})\) to be free.