Journal für die reine und angewandte Mathematik (Crelles Journal)· 2026Q1
Lower Ricci curvature bounds and the orientability of spaces
- 1citations
- Q1SCImago
- 2026year
Short summary
Spaces with Ricci curvature bounded below are shown to be orientable if their manifold part is orientable, extending previous theories and proving uniform local orientability for non-collapsing four-manifolds with Ricci curvature bounded below.
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Key points
- Establishes equivalent characterizations of orientability for Ricci limit and RCD spaces based on their manifold part.
- Proves a new stability theorem for spaces with Ricci curvature bounded below.
- Deduces uniform local orientability for four-manifolds with Ricci curvature bounded below and non-collapsing volume.
- Shows that four-manifolds with nonnegative Ricci curvature and Euclidean volume growth are orientable.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Journal für die reine und angewandte Mathematik (Crelles Journal), 2026 · DOI ↗
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