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Curvature, diameter and bounded Betti numbers
We consider the image of the comparison homomorphism from bounded cohomology to ordinary cohomology. Its dimension is called the bounded Betti number. In our earlier work we proved that the total bounded Betti number of a closed Riemannian $n$-manifold satisfying $\Ric\geq -(n-1)$ and $\Diam\leq D$
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