A Rational Model for the Evaluation Map

Abstract

Abstract Let 𝑋 be an 𝑙-connected space and 𝑈 a connected CW complex with dim 𝑈 ≤ 𝑙. Let 𝐹(𝑈,𝑋) be the space of continuous maps from 𝑈 to 𝑋. In this paper, an algebraic model for the evaluation map 𝐹(𝑈,𝑋) × 𝑈 → 𝑋 is considered in terms of the model for the function space due to Brown and Szczarba [Trans. Amer. Math. Soc. 349: 4931-4951, 1997]. It turns out that the Brown and Szczarba model for the function space coincides with Haefliger's model.