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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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Spaces which look like quaternionic projective $n$-space
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by C. A. McGibbon PDF
Trans. Amer. Math. Soc. 272 (1982), 569-587 Request permission

Abstract:

The projective $n$-spaces which correspond to the various multiplicative structures on the three sphere are studied. Necessary and sufficient conditions for a projective $n$-space to extend to a projective $n+1$-space are described. At each odd prime, an infinite family of exotic projective spaces is constructed. These exotic spaces are not homotopy equivalent, at the prime in question, to the classical quaternionic projective $n$-space. It is also shown that these exotic projective $n$-spaces do not occur as the finite skeleton of a classifying space for a group with the homotopy type of the three sphere.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 272 (1982), 569-587
  • MSC: Primary 55R35
  • DOI: https://doi.org/10.1090/S0002-9947-1982-0662054-0
  • MathSciNet review: 662054