On phantom maps into co-H–spaces

Schwass, James

doi:10.2140/agt.2017.17.847

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On phantom maps into co-H–spaces

James Schwass

Algebraic & Geometric Topology 17 (2017) 847–867

DOI: 10.2140/agt.2017.17.847

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 $H_{i} (Y; ℚ) \neq 0$ 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

References

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

Volume 17, issue 2 (2017)