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Proceedings of the American Mathematical Society

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

 

 

Positive scalar curvature and $ K{\rm O}$-characteristic numbers


Author: Hitoshi Moriyoshi
Journal: Proc. Amer. Math. Soc. 100 (1987), 585-588
MSC: Primary 57R15; Secondary 53C21
MathSciNet review: 891168
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Abstract: Let $ M$ be an $ (8k + 2)$-dimensional closed spin manifold and $ N$ an orientable hypersurface of $ M$ with the induced spin structure. If $ M$ admits a metric with positive scalar curvature and $ N$ represents a nonzero homology class of $ {H_{8k + 1}}(M;{\mathbf{Z}})$, then the KO-characteristic number $ \alpha (N)$ vanishes. This result relates to the conjecture by Gromov and Lawson on the vanishing of higher $ \hat A$-genera.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0891168-5
Keywords: KO-characteristic number, positive scalar curvature
Article copyright: © Copyright 1987 American Mathematical Society