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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Orientable products in $ \mathcal{N}$


Author: Howard Osborn
Journal: Proc. Amer. Math. Soc. 90 (1984), 167-170
MSC: Primary 57R75; Secondary 57R20
MathSciNet review: 722438
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0722438-6
PII: S 0002-9939(1984)0722438-6
Keywords: Product manifolds, unoriented cobordism, orientability
Article copyright: © Copyright 1984 American Mathematical Society