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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Construction of manifolds of positive scalar curvature


Author: Rodney Carr
Journal: Trans. Amer. Math. Soc. 307 (1988), 63-74
MSC: Primary 53C20
DOI: https://doi.org/10.1090/S0002-9947-1988-0936805-7
MathSciNet review: 936805
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Abstract: We prove that a regular neighborhood of a codimension $ \geqslant 3$ subcomplex of a manifold can be chosen so that the induced metric on its boundary has positive scalar curvature. A number of useful facts concerning manifolds of positive scalar curvature follow from this construction. For example, we see that any finitely presented group can appear as the fundamental group of a compact $ 4$-manifold with such a metric.


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

  • [GL] M. Gromov and H. B. Lawson, The classification of simply connected manifolds of positive scalar curvature, Ann. of Math. 111 (1980), 423-434. MR 577131 (81h:53036)
  • [HNK] F. Hirzebruch, W. D. Neumann and S. S. Koh, Differentiable manifolds and quadratic forms, Lecture Notes in Pure and Appl. Math., Vol. 4, Deker, 1971. MR 0341499 (49:6250)
  • [SY] R. Schoen and S. T. Yau, On the structure of manifolds with positive scalar curvature, Manuscripta Math. 28 (1979), 159-183. MR 535700 (80k:53064)

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DOI: https://doi.org/10.1090/S0002-9947-1988-0936805-7
Article copyright: © Copyright 1988 American Mathematical Society

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