## Algebraic & Geometric Topology

### On phantom maps into co-H–spaces

James Schwass

#### 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 $Hi(Y ; ℚ)≠0$ 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 17, Number 2 (2017), 847-867.

Dates
Received: 17 August 2015
Revised: 9 March 2016
Accepted: 9 July 2016
First available in Project Euclid: 19 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1508431446

Digital Object Identifier
doi:10.2140/agt.2017.17.847

Mathematical Reviews number (MathSciNet)
MR3623674

Zentralblatt MATH identifier
1364.55011

Subjects
Primary: 55P45: $H$-spaces and duals 55S37: Classification of mappings

Keywords
phantom maps co-H–spaces

#### Citation

Schwass, James. On phantom maps into co-H–spaces. Algebr. Geom. Topol. 17 (2017), no. 2, 847--867. doi:10.2140/agt.2017.17.847. https://projecteuclid.org/euclid.agt/1508431446

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