Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Simply connected spin manifolds with positive scalar curvature


Author: Tetsuro Miyazaki
Journal: Proc. Amer. Math. Soc. 93 (1985), 730-734
MSC: Primary 53C20; Secondary 57R75
DOI: https://doi.org/10.1090/S0002-9939-1985-0776211-4
MathSciNet review: 776211
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {l_n}$ be equal to 2 or 4 according as $ n$ is congruent $ \mod 8$ to zero or not. If the $ \hat A$-genus of a compact simply connected spin manifold of dimension $ n \geqslant 5$ vanishes, then the connected sum of $ {l_n}$ copies of the manifold admits a metric of positive scalar curvature. This supports a conjecture of Gromov and Lawson.


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

  • [1] D. W. Anderson, E. H. Brown, Jr. and F. P. Peterson, The structure of the spin cobordism ring, Ann. of Math. (2) 83 (1966), 47-53.
  • [2] L. B. Bergery, La coubure scalaire des variétés riemanniennes, (Séminaire Bourbaki, 32e année, 1979/80, no. 556), Lecture Notes in Math., vol. 842, Springer-Verlag, Berlin and New York, pp. 225-245. MR 636526 (84f:53032)
  • [3] A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces. I. Amer. J. Math. 8 (1958), 458-538. MR 0102800 (21:1586)
  • [4] M. Gromov and H. B. Lawson, Jr., The classification of simply connected manifolds of positive scalar curvature, Ann. of Math. (2) 111 (1980), 423-434. MR 577131 (81h:53036)
  • [5] N. Hitchin, Harmonic spinours, Adv. in Math. 14 (1974), 1-55. MR 0358873 (50:11332)
  • [6] A. Lichnerowicz, Spineurs harmoniques, C. R. Acad. Sci. Paris Sér. I Math. 257 (1963), 7-9. MR 0156292 (27:6218)
  • [7] J. Milnor, Remarks concerning spin manifolds, Differential Geometry and Combinatorial Topology, Princeton Univ. Press, Princeton, N. J., 1965, pp. 55-62. MR 0180978 (31:5208)
  • [8] B. O'Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459-469. MR 0200865 (34:751)
  • [9] R. H. Szczarba, On tangent bundles of fiber spaces and quotient spaces, Amer. J. Math. 86 (1964), 685-697. MR 0172303 (30:2522)
  • [10] R. Stong, Notes on cobordism theory, Princeton Univ. Press, Princeton, N. J., 1968. MR 0248858 (40:2108)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C20, 57R75

Retrieve articles in all journals with MSC: 53C20, 57R75


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0776211-4
Keywords: Positive scalar curvature, spin cobordism
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society