Gromov–Hausdorff limits of aspherical manifolds
Abstract
Let X be a compact Gromov-Hausdorff limit space of a sequence of compact n-manifolds, M i , of Ricci curvature Ric M i .n1/, volume vol.M i / !0, and where all points in M i are .ı;/-local rewinding Reifenberg points, or the sectional curvature satisfies sec M i 1, respectively.We conjecture that if M i 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.Our main result asserts that if M i is diffeomorphic or homeomorphic to a nilmanifold, then X is diffeomorphic or homeomorphic to a nilmanifold, respectively.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Geometric and Algebraic Topology
Geometry and complex manifolds
Publication details
- Journal / source
- Geometry & Topology
- Volume
- 30
- Issue
- 7
- Pages
- 2685–2712
- Publication date
- 13 August 2026
- Language
- EN