#### Volume 17, issue 2 (2017)

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On phantom maps into co-H–spaces

### James Schwass

Algebraic & Geometric Topology 17 (2017) 847–867
##### 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 ${H}_{i}\left(Y;ℚ\right)\ne 0$ 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.

##### Keywords
phantom maps, co-H–spaces
##### Mathematical Subject Classification 2010
Primary: 55P45, 55S37
##### Publication
Received: 17 August 2015
Revised: 9 March 2016
Accepted: 9 July 2016
Published: 14 March 2017
##### Authors
 James Schwass Grand Rapids, MI 49503 United States