Abstract
A complete classification of stable homotopy types of complex and quaternionic stunted projective spaces, denoted by C P n k {\mathbf {C}}P_n^k and Q P n k {\mathbf {Q}}P_n^k respectively, is obtained. The necessary conditions for such equivalences are found using K-theory and various characteristic classes introduced originally by J. F. Adams. As a by-product one finds the J-orders of the Hopf bundles over C P n {\mathbf {C}}{P^n} and Q P n {\mathbf {Q}}{P^n} respectively. The algebraic part is rather involved. Finally a homotopy theoretical argument yields the constructions of such homotopy equivalences as are allowed by the fulfillment of the necessary conditions.
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