Phantom Maps and Homology Theories

J. Daniel Christensen; Neil P. Strickland

doi:10.1016/s0040-9383(97)00031-1

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arXiv · math/9802008

Phantom Maps and Homology Theories

J. Daniel Christensen·Neil P. Strickland

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Abstract

We study phantom maps and homology theories in a stable homotopy category S via a certain Abelian category A. We express the group P(X,Y) of phantom maps X -> Y as an Ext group in A, and give conditions on X or Y which guarantee that it vanishes. We also determine P(X,HB). We show that any composite of two phantom maps is zero, and use this to reduce Margolis's axiomatisation conjecture to an extension problem. We show that a certain functor S -> A is the universal example of a homology theory with values in an AB 5 category and compare this with some results of Freyd.

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BibTeX RIS

J. Daniel Christensen, Neil P. Strickland. 1998-02-02. Phantom Maps and Homology Theories. https://doi.org/10.1016/s0040-9383(97)00031-1

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