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Proceedings of the American Mathematical Society

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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.

References [Enhancements On Off] (What's this?)

  • [1] M. F. Atiyah and I. M. Singer, The index of elliptic operators. V, Ann. of Math. 93 (1971), 139-149. MR 0279834 (43:5555)
  • [2] M. Gromov and H. B. Lawson, Jr., Spin and scalar curvature in the presence of a fundamental group. I, Ann. of Math. 111 (1980), 423-434. MR 577131 (81h:53036)
  • [3] N. Hitchin, Harmonic spinors, Adv. in Math. 14 (1974), 1-55. MR 0358873 (50:11332)

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Keywords: KO-characteristic number, positive scalar curvature
Article copyright: © Copyright 1987 American Mathematical Society

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