Positive scalar curvature and -characteristic numbers
Proc. Amer. Math. Soc. 100 (1987), 585-588
Primary 57R15; Secondary 53C21
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Abstract: Let be an -dimensional closed spin manifold and an orientable hypersurface of with the induced spin structure. If admits a metric with positive scalar curvature and represents a nonzero homology class of , then the KO-characteristic number vanishes. This result relates to the conjecture by Gromov and Lawson on the vanishing of higher -genera.
F. Atiyah and I.
M. Singer, The index of elliptic operators. V, Ann. of Math.
(2) 93 (1971), 139–149. MR 0279834
Gromov and H.
Blaine Lawson Jr., The classification of simply connected manifolds
of positive scalar curvature, Ann. of Math. (2) 111
(1980), no. 3, 423–434. MR 577131
Hitchin, Harmonic spinors, Advances in Math.
14 (1974), 1–55. MR 0358873
- M. F. Atiyah and I. M. Singer, The index of elliptic operators. V, Ann. of Math. 93 (1971), 139-149. MR 0279834 (43:5555)
- 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)
- N. Hitchin, Harmonic spinors, Adv. in Math. 14 (1974), 1-55. MR 0358873 (50:11332)
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