2025/03/29 by Rong, Xiaochun · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.23107
Let X be a compact Gromov-Hausdorff limit space of a collapsing sequence of compact n-manifolds, Mi, of Ricci curvature RicMi≥ -(n-1) and all points in Mi are (δ,ρ)-local rewinding Reifenberg points, or sectional curvature secMi≥ -1, respectively. We conjecture that if Mi is an aspherical manifold of fundamental group satisfying a certain condition (e.g., a nilpotent group), then X is a differentiable, or topological aspherical manifold, respectively. A main result in this paper asserts that if Mi a diffeomorphic or homeomorphic to a nilmanifold, then X is diffeomorphic or homeomorphic to a nilmanifold, respectively.