| Summary: | In this paper, we construct a pyramid Ricci flow starting with a complete Riemannian manifold (Mn,g0) that is PIC1, or more generally satisfies a lower curvature bound KIC1≥−α0. That is, instead of constructing a flow on M×[0,T], we construct it on a subset of space-time that is a union of parabolic cylinders Bg0(x0,k)×[0,Tk] for each k∈N, where Tk↓0, and prove estimates on the curvature and Riemannian distance. More generally, we construct a pyramid Ricci flow starting with any noncollapsed IC1-limit space, and use it to establish that such limit spaces are globally homeomorphic to smooth manifolds via homeomorphisms that are locally bi-Hölder.
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