Homotopy type finiteness theorems for certain precompact families of Riemannian manifolds

Yamaguchi, Takao

doi:10.1090/S0002-9939-1988-0928999-X

Homotopy type finiteness theorems for certain precompact families of Riemannian manifolds
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Proc. Amer. Math. Soc. 102 (1988), 660-666 Request permission

Abstract:

In this paper, we consider a precompact family of Riemannian manifolds with respect to the Hausdorff distance, and prove the homotopy type finiteness of elements in the family. This is an extension in the homotopy type version of the Cheeger and Weinstein finiteness theorems.

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