Instability of the fundamental group for non-collapsed Ricci-limits
Differential Geometry
2025-05-26 v1
Abstract
We construct two sequences of closed -dimensional manifolds with non-negative Ricci curvature, diameter bounded from above by , and volume bounded from below by , with different fundamental groups but with the same Gromov-Hausdorff limit. This provides a negative answer to the question posed in [J. Pan. Ricci Curvature and Fundamental Groups of Effective Regular Sets. Journal of Mathematical Study, 58(1):3--21, 2025].
Cite
@article{arxiv.2505.17263,
title = {Instability of the fundamental group for non-collapsed Ricci-limits},
author = {Camillo Brena},
journal= {arXiv preprint arXiv:2505.17263},
year = {2025}
}