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# Homology, Homotopy and Applications

## Volume 6 (2004)

### Number 1

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

Pages: 341 – 350

DOI: http://dx.doi.org/10.4310/HHA.2004.v6.n1.a18

#### Author

#### Abstract

In this paper, for a formal, path connected, finite-dimensional 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 $H^*(\mathcal{F}_*(X,Y);\mathbb{Q})$ of the function space $\mathcal{F}_*(X,Y)$ of based maps to be free.

#### Keywords

rational cohomology, function spaces, free commutative graded algebras, formal spaces

#### 2010 Mathematics Subject Classification

Primary 55P62. Secondary 54C40.