Phantom Maps and Homology Theories

Details Phantom Maps and Homology Theories Phantom Maps and Homology Theories

1998-02-02

arxiv.org/abs/math/9802008v1

Mathematics

Algebraic Topology

25 pages, AMSLaTeX, to appear in Topology

Scientific paper

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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