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The classification of stunted projective spaces by stable homotopy type


Authors: S. Feder and S. Gitler
Journal: Trans. Amer. Math. Soc. 225 (1977), 59-81
MSC: Primary 55D15
DOI: https://doi.org/10.1090/S0002-9947-1977-0423338-2
MathSciNet review: 0423338
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Abstract: A complete classification of stable homotopy types of complex and quaternionic stunted projective spaces, denoted by $ {\mathbf{C}}P_n^k$ and $ {\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 $ {\mathbf{C}}{P^n}$ and $ {\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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0423338-2
Keywords: Projective space, stunted projective space, Thom space, J-order, K-theory, spherical fibrations
Article copyright: © Copyright 1977 American Mathematical Society

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