Lower Ricci curvature bounds and the orientability of spaces
Abstract
Abstract We study orientability in spaces with Ricci curvature bounded below. Building on the theory developed by Honda, we establish equivalent characterizations of orientability for Ricci limit and RCD \mathrm{RCD} spaces in terms of the orientability of their manifold part. We prove a new stability theorem and, as a corollary, we deduce that four-manifolds with Ricci curvature bounded below and volume non-collapsing are uniformly locally orientable. As a global counterpart of the latter, we show that four-manifolds with nonnegative Ricci curvature and Euclidean volume growth are orientable.
Fields of Study & Subjects
Advanced Differential Geometry Research
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Publication details
- Journal / source
- Journal für die reine und angewandte Mathematik (Crelles Journal)
- Publisher
- Walter de Gruyter GmbH
- Publication date
- 22 September 2026
- Language
- EN