Phantom Maps and Homology Theories
         
            J. Daniel Christensen and Neil P. Strickland


Keywords: phantom map, stable homotopy theory, spectrum, 
          triangulated category

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'
    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.