We study the existence of essential phantom maps into co-H–spaces, motivated by Iriye’s observation that every suspension space of finite type with for some 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.
"On phantom maps into co-H–spaces." Algebr. Geom. Topol. 17 (2) 847 - 867, 2017. https://doi.org/10.2140/agt.2017.17.847