The more modest goal of this paper is to give a characterization of the maps which induce the zero homomorphism on homotopy groups. Here the result is not so simple, and the answer is given in terms of the Postnikov systems of the spaces involved. These maps occur in various cases, but for the purpose of illustration we consider the following two:n1) The question of when such a map is null-homotopic andn2) the example when the image space is Bu, the classifying space for the infinite unitary group.
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