Construction of manifolds of positive scalar curvature
HTML articles powered by AMS MathViewer
- by Rodney Carr PDF
- Trans. Amer. Math. Soc. 307 (1988), 63-74 Request permission
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
- 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. MR 577131, DOI 10.2307/1971103
- F. Hirzebruch, W. D. Neumann, and S. S. Koh, Differentiable manifolds and quadratic forms, Lecture Notes in Pure and Applied Mathematics, Vol. 4, Marcel Dekker, Inc., New York, 1971. Appendix II by W. Scharlau. MR 0341499
- R. Schoen and S. T. Yau, On the structure of manifolds with positive scalar curvature, Manuscripta Math. 28 (1979), no. 1-3, 159–183. MR 535700, DOI 10.1007/BF01647970
Additional Information
- © Copyright 1988 American Mathematical Society
- 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