**Katsuhiko Kuribayashi**

## A Rational Model for the Evaluation Map

**Abstract:**

Let $X$ be an $l$-connected space and $U$ a connected CW complex with $\dim U \leq
l$. Let ${\mathcal F}(U, X)$ be the space of continuous maps from $U$ to $X$. In
this paper, an algebraic model for the evaluation map ${\mathcal F}(U, X) \times
U \to X$ is considered in terms of the model for the function space due to Brown
and Szczarba (Trans. Amer. Math. Soc. **349** (1997), No. 12). It
turns out that the Brown and Szczarba model for the function space coincides
with Haefliger's model.

**Keywords:**

Evaluation maps, function spaces, Sullivan models.

**MSC 2000:** 18G30, 55P62