Stolz, Stephan Simply connected manifolds of positive scalar curvature. (English) Zbl 0719.53018 Bull. Am. Math. Soc., New Ser. 23, No. 2, 427-432 (1990). Using techniques from stable homotopy theory, the author proves that if M is a spin manifold with positive scalar curvature, then the KO- characteristic number \(\alpha\) (M) vanishes. Reviewer: H.Özekes (İstanbul) Cited in 4 Documents MSC: 53C20 Global Riemannian geometry, including pinching 55T15 Adams spectral sequences 57R90 Other types of cobordism 55N22 Bordism and cobordism theories and formal group laws in algebraic topology Keywords:stable homotopy theory; spin manifold; positive scalar curvature; characteristic number PDFBibTeX XMLCite \textit{S. Stolz}, Bull. Am. Math. Soc., New Ser. 23, No. 2, 427--432 (1990; Zbl 0719.53018) Full Text: DOI References: [1] J. F. Adams and S. B. Priddy, Uniqueness of \?\?\?, Math. Proc. Cambridge Philos. Soc. 80 (1976), no. 3, 475 – 509. · Zbl 0338.55011 · doi:10.1017/S0305004100053111 [2] D. W. Anderson, E. H. Brown Jr., and F. P. Peterson, The structure of the Spin cobordism ring, Ann. of Math. (2) 86 (1967), 271 – 298. · Zbl 0156.21605 · doi:10.2307/1970690 [3] Arthur L. Besse, Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 10, Springer-Verlag, Berlin, 1987. · Zbl 0613.53001 [4] J. M. Boardman, Stable homotopy theory; Chapter V-Duality and Thorn spectra, mimeographed notes, Warwick, 1966. [5] Mikhael 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. · Zbl 0463.53025 · doi:10.2307/1971103 [6] Nigel Hitchin, Harmonic spinors, Advances in Math. 14 (1974), 1 – 55. · Zbl 0284.58016 · doi:10.1016/0001-8708(74)90021-8 [7] M. Kreck and S. Stolz, A geometric interpretation of elliptic homology (in preparation). · Zbl 0851.55007 [8] André Lichnerowicz, Spineurs harmoniques, C. R. Acad. Sci. Paris 257 (1963), 7 – 9 (French). · Zbl 0136.18401 [9] H. R. Margolis, Eilenberg-Mac Lane spectra, Proc. Amer. Math. Soc. 43 (1974), 409 – 415. · Zbl 0284.55014 [10] Tetsuro Miyazaki, Simply connected spin manifolds with positive scalar curvature, Proc. Amer. Math. Soc. 93 (1985), no. 4, 730 – 734. · Zbl 0581.55001 [11] D. J. Pengelley, \(H^{*} (M{\mathrm O}{\l}angle 8\rangle ;\,Z/2)\) is an extended \(A^{*} _{2}\)-coalgebra, , Proc. Amer. Math. Soc. 87 (1983), 355-356. · Zbl 0517.55012 [12] Jonathan Rosenberg, \?*-algebras, positive scalar curvature, and the Novikov conjecture. III, Topology 25 (1986), no. 3, 319 – 336. · Zbl 0605.53020 · doi:10.1016/0040-9383(86)90047-9 [13] R. M. Switzer, Algebraic topology-homotopy and homology, Springer-Verlag, Berlin and New York, 1975. · Zbl 0305.55001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.