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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Betti numbers of Alexandrov spaces
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by Liang-Khoon Koh PDF
Proc. Amer. Math. Soc. 122 (1994), 247-252 Request permission

Abstract:

We obtain a uniform bound on the sum of Betti numbers for a class of complete Alexandrov spaces with narrow ends.
References
  • U. Abresch, Lower curvature bounds, Toponogov’s theorem, and bounded topology. II, Ann. Sci. École Norm. Sup. (4) 20 (1987), no. 3, 475–502. MR 925724
  • Michael Gromov, Curvature, diameter and Betti numbers, Comment. Math. Helv. 56 (1981), no. 2, 179–195. MR 630949, DOI 10.1007/BF02566208
  • —, Structures métriques pour les variétés Riemanniennes, Cedic Fernand-Nathan, Paris, 1981. Z. Liu and Z. Shen, On the Betti numbers of Alexandrov spaces, preprint. G. Perelman, Alexandrov’s spaces with curvature bounded from below, II, preprint.
  • Ji-Ping Sha and DaGang Yang, Examples of manifolds of positive Ricci curvature, J. Differential Geom. 29 (1989), no. 1, 95–103. MR 978078
  • Ji-Ping Sha and DaGang Yang, Positive Ricci curvature on the connected sums of $S^n\times S^m$, J. Differential Geom. 33 (1991), no. 1, 127–137. MR 1085137
  • Z. Shen, Finite topological type and vanishing theorems for Riemannian manifolds, Ph.D. Thesis, SUNY Stony Brook. M. Gromov, Y. Burago, and G. Perelman, Alexandrov’s spaces with curvature bounded from below, preprint.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 122 (1994), 247-252
  • MSC: Primary 53C23; Secondary 53C20
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1195481-X
  • MathSciNet review: 1195481