Surgery and positive Bakry-Émery Ricci curvature
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917848579833856 |
|---|---|
| author | Reiser, Philipp Tripaldi, Francesca |
| author_facet | Reiser, Philipp Tripaldi, Francesca |
| contents | We consider the problem of preserving weighted Riemannian metrics of positive Bakry-Émery Ricci curvature along surgery. We establish two theorems of this type: One for connected sums, and one for surgeries along higher-dimensional spheres. In contrast to known surgery results for positive Ricci curvature, these results are local, i.e. we only impose assumptions on the weighted metric locally around the sphere along which the surgery is performed. As application we then show that all closed, simply-connected spin 5-manifolds admit a weighted Riemannian metric of positive Bakry-Émery Ricci curvature. By a result of Lott, this also provides new examples of manifolds with a Riemannian metric of positive Ricci curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18859 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Surgery and positive Bakry-Émery Ricci curvature Reiser, Philipp Tripaldi, Francesca Differential Geometry Geometric Topology Metric Geometry 53C20, 53C21, 54E35, 57R65 We consider the problem of preserving weighted Riemannian metrics of positive Bakry-Émery Ricci curvature along surgery. We establish two theorems of this type: One for connected sums, and one for surgeries along higher-dimensional spheres. In contrast to known surgery results for positive Ricci curvature, these results are local, i.e. we only impose assumptions on the weighted metric locally around the sphere along which the surgery is performed. As application we then show that all closed, simply-connected spin 5-manifolds admit a weighted Riemannian metric of positive Bakry-Émery Ricci curvature. By a result of Lott, this also provides new examples of manifolds with a Riemannian metric of positive Ricci curvature. |
| title | Surgery and positive Bakry-Émery Ricci curvature |
| topic | Differential Geometry Geometric Topology Metric Geometry 53C20, 53C21, 54E35, 57R65 |
| url | https://arxiv.org/abs/2410.18859 |