# 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

Available as: dvi dvi.gz ps ps.gz pdf