Phantom Maps and Homology Theories

Preprint

2 February 1998

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/9802008

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.

Keywords

MAPS AND HOMOLOGY
HOMOTOPY CATEGORY
HOMOLOGY THEORY
STABLE HOMOTOPY
STUDY PHANTOM
PHANTOM MAPS

All Related Versions

Version 1, 1998-02-02, ArXiv
Published version: Topology, 37 (2), 339.

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