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Curvature, Diameter and Bounded Betti Numbers.
- Source :
-
Chinese Annals of Mathematics . Apr2006, Vol. 27 Issue 2, p143-152. 10p. - Publication Year :
- 2006
-
Abstract
- In this paper, we introduce the notion of bounded Betti numbers, and show that the bounded Betti numbers of a closed Riemannian n-manifold (M,g) with Ric (M)≥ -(n - 1) and Diam (M)≤D are bounded by a number depending on D and n. We also show that there are only finitely many isometric isomorphism types of bounded cohomology groups (Ĥ*(M),ǁ · ǁ∞) among closed Riemannian manifold (M,g) with K(M)≥ -1 and Diam (M)≤D. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02529599
- Volume :
- 27
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Chinese Annals of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 22350928
- Full Text :
- https://doi.org/10.1007/s11401-005-0398-z