Instability of the fundamental group for non-collapsed Ricci-limits
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916754473615360 |
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| author | Brena, Camillo |
| author_facet | Brena, Camillo |
| contents | We construct two sequences of closed $4$-dimensional manifolds with non-negative Ricci curvature, diameter bounded from above by $1$, and volume bounded from below by $v>0$, 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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17263 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Instability of the fundamental group for non-collapsed Ricci-limits Brena, Camillo Differential Geometry We construct two sequences of closed $4$-dimensional manifolds with non-negative Ricci curvature, diameter bounded from above by $1$, and volume bounded from below by $v>0$, 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]. |
| title | Instability of the fundamental group for non-collapsed Ricci-limits |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2505.17263 |