Intermediate Ricci Curvatures and Gromov’s Betti number bound
DOKPE
- Reiser, Philipp ORCID University of Fribourg
- Wraith, David J. Maynooth University
- 20.09.2023
Published in:
- The Journal of Geometric Analysis. - Springer Science and Business Media LLC. - 2023, vol. 33, no. 12
English
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.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
-
- English
- Classification
- Mathematics
- License
- CC BY
- Open access status
- hybrid
- Identifiers
-
- DOI 10.1007/s12220-023-01423-6
- ISSN 1050-6926
- Persistent URL
- https://folia.unifr.ch/unifr/documents/326114
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