Curvature, diameter and betti numbers

Mikhael Gromov

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)179-195
Number of pages17
JournalCommentarii Mathematici Helvetici
Volume56
Issue number1
DOIs
StatePublished - Dec 1981

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Betti numbers
Sectional Curvature
Curvature
Nonnegative Curvature
Compact Manifold
Riemannian Manifold
Lower bound
Upper bound
Metric
Estimate

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Curvature, diameter and betti numbers. / Gromov, Mikhael.

In: Commentarii Mathematici Helvetici, Vol. 56, No. 1, 12.1981, p. 179-195.

Research output: Contribution to journalArticle

Gromov, Mikhael. / Curvature, diameter and betti numbers. In: Commentarii Mathematici Helvetici. 1981 ; Vol. 56, No. 1. pp. 179-195.
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