Curvature, diameter and betti numbers

Michael 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

ASJC Scopus subject areas

  • Mathematics(all)

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