Intermediate Ricci curvatures and Gromov's Betti number bound
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916452118822912 |
|---|---|
| author | Reiser, Philipp Wraith, David J. |
| author_facet | Reiser, Philipp Wraith, David J. |
| contents | We consider intermediate Ricci curvatures $Ric_k$ on a closed Riemannian manifold $M^n$. These interpolate between the Ricci curvature when $k=n-1$ and the sectional curvature when $k=1$. By establishing a surgery result for Riemannian metrics with $Ric_k>0$, we show that Gromov's upper Betti number bound for sectional curvature bounded below fails to hold for $Ric_k>0$ when $\lfloor n/2 \rfloor+2 \le k \le n-1$. This was previously known only in the case of positive Ricci curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_13438 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Intermediate Ricci curvatures and Gromov's Betti number bound Reiser, Philipp Wraith, David J. Differential Geometry 53C20 We consider intermediate Ricci curvatures $Ric_k$ on a closed Riemannian manifold $M^n$. These interpolate between the Ricci curvature when $k=n-1$ and the sectional curvature when $k=1$. By establishing a surgery result for Riemannian metrics with $Ric_k>0$, we show that Gromov's upper Betti number bound for sectional curvature bounded below fails to hold for $Ric_k>0$ when $\lfloor n/2 \rfloor+2 \le k \le n-1$. This was previously known only in the case of positive Ricci curvature. |
| title | Intermediate Ricci curvatures and Gromov's Betti number bound |
| topic | Differential Geometry 53C20 |
| url | https://arxiv.org/abs/2208.13438 |