Algebraic & Geometric Topology

On phantom maps into co-H–spaces

James Schwass

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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 ; )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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

phantom maps co-H–spaces


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.

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