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 numb...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 （H（M）,Ⅱ·Ⅱ∞） among closed Riemannian manifold （M, g） with K（M） ≥ -1 and Diam （M） ≤ D.展开更多
文摘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 （H（M）,Ⅱ·Ⅱ∞） among closed Riemannian manifold （M, g） with K（M） ≥ -1 and Diam （M） ≤ D.
