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| Curvature, Diameter and Bounded Betti Numbers |
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Citation： |
Zhongmin SHEN,Jyh-Yang WU.Curvature, Diameter and Bounded Betti Numbers[J].Chinese Annals of Mathematics B,2006,27(2):143~152 |
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Net amount： 1081 |
Authors： |
Zhongmin SHEN; Jyh-Yang WU |
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| 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\,$(M)\ge -(n-1)$ and Diam\,$(M)\le
D$ 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 $({\widehat{\text H}}^*(M), \parallel
\cdot\parallel_{\infty})$ among closed Riemannian manifold $(M,
g)$ with $K(M)\ge -1$ and Diam\,$(M)\le D$. |
Keywords： |
Diameter, Ricci curvature, Sectional curvature, Bounded cohomology,
Bounded Betti number |
Classification： |
53C21, 53C23 |
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