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