Georgian Mathematical Journal 13 (2006), No. 1, 127--141
Copyright Heldermann Verlag 2006
A Rational Model for the Evaluation Map
Katsuhiko Kuribayashi
Dept. of Mathematical Sciences, Faculty of Science, Shinshu University, Matsumoto, Nagano 390-8621, Japan
kuri@math.shinshu-u.ac.jp
[Abstract-pdf]
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 E. H. Brown and R. H. Szczarba [Trans. Amer. Math. Soc. 349 (1997) 4931--4951]. 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: 18G30, 55P62
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