Curvature, diameter and betti numbers

Michael Gromov

Research output: Contribution to journalArticlepeer-review


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
Issue number1
StatePublished - Dec 1981

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'Curvature, diameter and betti numbers'. Together they form a unique fingerprint.

Cite this