On phantom maps into co-H–spaces

Abstract

We study the existence of essential phantom maps into co-H–spaces, motivated by Iriye’s observation that every suspension space $Y$ of finite type with $H_i\left(Y;\mathbb{Q}\right)\ne 0$ for some $i>1$ is the target of essential phantom maps. We show that Iriye’s observation can be extended to the collection of nilpotent, finite-type co-H–spaces. This work hinges on an enhanced understanding of the connections between homotopy decompositions of looped co-H–spaces and coalgebra decompositions of tensor algebras due to Grbic̀, Theriault and Wu.