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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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The stable geometric dimension of vector bundles over real projective spaces
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by Donald M. Davis, Sam Gitler and Mark Mahowald PDF
Trans. Amer. Math. Soc. 268 (1981), 39-61 Request permission

Correction: Trans. Amer. Math. Soc. 280 (1983), 841-843.

Abstract:

An elementary argument shows that the geometric dimension of any vector bundle of order ${2^e}$ over $R{P^n}$ depends only on $e$ and the residue of $n \bmod 8$ for $n$ sufficiently large. In this paper we calculate this geometric dimension, which is approximately $2e$. The nonlifting results are easily obtained using the spectrum $bJ$. The lifting results require $bo$-resolutions. Half of the paper is devoted to proving Mahowald’s theorem that beginning with the second stage $bo$-resolutions act almost like $K({Z_2})$-resolutions.
References
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 268 (1981), 39-61
  • MSC: Primary 55N15; Secondary 55R25
  • DOI: https://doi.org/10.1090/S0002-9947-1981-0628445-8
  • MathSciNet review: 628445