Towers and injective cohomology algebras

Abstract

Let Y Y be a space of finite type such that H ∗ Y {H^{\ast }}Y is injective as an unstable algebra over the Steenrod algebra A A and such that H ¯ ∗ Y {\overline H ^{\ast }}Y is A A -unbounded. Let X X be a simply connected p p -complete space. Then any map of A A -algebras f : H ∗ Ω X → H ∗ Y f:{H^{\ast }}\Omega X \to {H^{\ast }}Y can be realized as a map of spaces.