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Reiser, Philipp and Wraith, David J. (2023) Intermediate Ricci Curvatures and Gromov’s Betti number bound. The Journal of Geometric Analysis, 33 (12). ISSN 1050-6926
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Official URL: https://doi.org/10.1007/s12220-023-01423-6
Abstract
We consider intermediate Ricci curvatures Rick on a closed Riemannian manifold
Mn. 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
Rick > 0, we show that Gromov’s upper Betti number bound for sectional curvature
bounded below fails to hold for Rick > 0 when (n/2) + 2 ≤ k ≤ n − 1. This was
previously known only in the case of positive Ricci curvature (Sha and Yang in J Differ Geom 29(1):95–103, 1989, J Differ Geom 33:127–138, 1991).
| Item Type: | Article |
|---|---|
| Keywords: | Riemannian geometry; Intermediate Ricci curvatures; Surgery; Total Betti numbers; |
| Academic Unit: | Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: | 18872 |
| Identification Number: | 10.1007/s12220-023-01423-6 |
| Depositing User: | Dr. David Wraith |
| Date Deposited: | 12 Sep 2024 13:48 |
| Journal or Publication Title: | The Journal of Geometric Analysis |
| Publisher: | Springer US |
| Refereed: | Yes |
| Related URLs: | |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/18872 |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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