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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The classification of stunted projective spaces by stable homotopy type
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by S. Feder and S. Gitler PDF
Trans. Amer. Math. Soc. 225 (1977), 59-81 Request permission

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
  • © Copyright 1977 American Mathematical Society
  • 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