arXiv Open Access 2024

Lower Ricci Curvature Bounds and the Orientability of Spaces

Camillo Brena Elia Bruè Alessandro Pigati

Lihat Sumber

Abstrak

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 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.

Topik & Kata Kunci

math.DG

Penulis (3)

Camillo Brena

Elia Bruè

Alessandro Pigati

Format Sitasi

APA MLA BibTeX

Brena, C., Bruè, E., Pigati, A. (2024). Lower Ricci Curvature Bounds and the Orientability of Spaces. https://arxiv.org/abs/2412.19288

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓