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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 immersion conjecture for $RP^{8l+7}$ is false
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by Donald M. Davis and Mark Mahowald PDF
Trans. Amer. Math. Soc. 236 (1978), 361-383 Request permission

Abstract:

Let $\alpha (n)$ denote the number of l’s in the binary expansion of n. It is proved that if $n \equiv 7$ (8), $\alpha (n) = 6$, and $n \ne 63$, then ${\mathbf {R}}{P^n}$ can be immersed in ${{\mathbf {R}}^{2n - 14}}$. This provides the first counterexample to the well-known conjecture that the best immersion is in ${{\mathbf {R}}^{2n - 2\alpha (n) + 1}}$ (when $\alpha (n) \equiv 1$ or $2 \bmod 4$). The method of proof is obstruction theory.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 236 (1978), 361-383
  • MSC: Primary 57D40
  • DOI: https://doi.org/10.1090/S0002-9947-1978-0646070-X
  • MathSciNet review: 0646070