Some algebraic constructions in rational homotopy theory

✍ Scribed by Edgar H. Brown Jr; Robert H. Szczarba

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 420 KB
• Volume: 80
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(97)00012-6

✦ Synopsis

In this note we describe constructions in the category of differential graded commutative algebras over the rational numbers Q which are analogs of the space F(X. Y) of continuous maps of X to Y, the component 2=(X, Y, f) containing f E _T(X, Y), fibrations, induced fibrations, the space T(rr) of sections of a fibration T: E + X, and the component ~(K,o) containing o E r(rr). As a focus, we address the problem of expressing rr*(3(X, Y, f)) = Hom(rr, (3(X, Y, f)), Q) in terms of differential graded algebra models for X and Y.