Limit Spaces Of Riemannian Manifolds With Bounded Ricci Curvature

In this paper,we discuss the topological structure of limit spaces of compact Riemannian manifolds with bounded Ricci curvature and(δ,ρ)-Reifenberg local covering geometry.We find that the elements of the limit spaces are smooth in the homeomorphic sense and the Hausdorff dimension of the limit spaces is an integer by using the metric smoothing and the isometric action of Lie groups.Then,the singular fiber bundle from the manifolds to its collapsed space is obtained by studying the frame bundle.