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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Orientable products in $\mathcal {N}$
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by Howard Osborn PDF
Proc. Amer. Math. Soc. 90 (1984), 167-170 Request permission

Abstract:

It is well known that the square $W \times W$ of any smooth closed manifold $W$ is cobordant to an orientable manifold. This note shows more specifically that a product $U \times V$ of smooth closed manifolds $U$ and $V$ is cobordant to an orientable manifold if and only if there is a smooth closed manifold $W$ such that $U$ and $V$ are both products of $W$ by orientable manifolds.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 90 (1984), 167-170
  • MSC: Primary 57R75; Secondary 57R20
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0722438-6
  • MathSciNet review: 722438