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Curvature, diameter and betti numbers

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Commentarii Mathematici Helvetici

Abstract

We give an upper bound for the Betti numbers of a compact Riemannian manifold in terms of its diameter and the lower bound of the sectional curvatures. This estimate in particular shows that most manifolds admit no metrics of non-negative sectional curvature.

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Authors and Affiliations

  1. Institut des Hautes Etudes Scientifiques, 35, route de Chartres, 91440, Bures-sur-Yvette

    Michael Gromov

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  1. Michael Gromov
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Gromov, M. Curvature, diameter and betti numbers. Commentarii Mathematici Helvetici 56, 179–195 (1981). https://doi.org/10.1007/BF02566208

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  • DOI: https://doi.org/10.1007/BF02566208

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