We study the topological structure of Ricci limit spaces, which arise as Gromov–Hausdorff limits of manifolds with a uniform lower Ricci curvature bound. Our previous work focused on the local topology of Ricci limit spaces. In particular, we proved that any Ricci limit space is semi–locally simply connected. Our current work concerns the topological structure of sequences of collapsing manifolds. Under some mild assumptions, we show that these manifolds admit a fiber bundle structure and collapse along the fiber direction.
