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.References
- M. F. Atiyah and I. M. Singer, The index of elliptic operators. V, Ann. of Math. (2) 93 (1971), 139β149. MR 279834, DOI 10.2307/1970757
- Mikhael Gromov and H. Blaine Lawson Jr., The classification of simply connected manifolds of positive scalar curvature, Ann. of Math. (2) 111 (1980), no.Β 3, 423β434. MR 577131, DOI 10.2307/1971103
- Nigel Hitchin, Harmonic spinors, Advances in Math. 14 (1974), 1β55. MR 358873, DOI 10.1016/0001-8708(74)90021-8
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