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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Positive scalar curvature and $K\textrm {O}$-characteristic numbers
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by Hitoshi Moriyoshi PDF
Proc. Amer. Math. Soc. 100 (1987), 585-588 Request permission

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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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 100 (1987), 585-588
  • MSC: Primary 57R15; Secondary 53C21
  • DOI: https://doi.org/10.1090/S0002-9939-1987-0891168-5
  • MathSciNet review: 891168