Maps which Induce the Zero Map on Homotopy

Abstract

In this paper, all spaces will have the homotopy type of simply connected CW-complexes, and will have base points which are preserved by maps and homotopies. We denote by [X, Y] the set of homotopy classes of maps from X to Y, and by N[X, Y] the subset of those homotopy classes [ƒ] which induce the zero homomorphism on homotopy, that is, is the zero homomorphism for each i.