## On the number of diffeomorphism classes in a certain class of Riemannian manifolds.(English)Zbl 0566.53038

Cheeger’s finiteness theorem asserts that there are only finitely many diffeomorphism classes in the class of compact Riemannian manifolds M of dimension n, such that the curvature of M is between two given bounds - $$\Lambda$$ $${}^ 2_ 1$$ and $$+ \Lambda^ 2_ 2$$ and diameter(M)$$\leq D$$, volume(M)$$\geq V$$, where D and V are given. Extensions of this result to complete manifolds are discussed.
Reviewer: W.Ballmann

### MSC:

 53C20 Global Riemannian geometry, including pinching 57R55 Differentiable structures in differential topology
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### References:

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