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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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Some immersion theorems for manifolds
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by A. Duane Randall PDF
Trans. Amer. Math. Soc. 156 (1971), 45-58 Request permission

Abstract:

In this paper we obtain several results on immersing manifolds into Euclidean spaces. For example, a spin manifold ${M^n}$ immerses in ${R^{2n - 3}}$ for dimension $n \equiv 0\bmod 4$ and n not a power of 2. A spin manifold ${M^n}$ immerses in ${R^{2n - 4}}$ for $n \equiv 7\bmod 8$ and $n > 7$. Let ${M^n}$ be a 2-connected manifold for $n \equiv 6\bmod 8$ and $n > 6$ such that ${H_3}(M;Z)$ has no 2-torsion. Then M immerses in ${R^{2n - 5}}$ and embeds in ${R^{2n - 4}}$. The method of proof consists of expressing k-invariants in Postnikov resolutions for the stable normal bundle of a manifold by means of higher order cohomology operations. Properties of the normal bundle are used to evaluate the operations.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 156 (1971), 45-58
  • MSC: Primary 57.20
  • DOI: https://doi.org/10.1090/S0002-9947-1971-0286121-1
  • MathSciNet review: 0286121