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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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 |
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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: | https://doi.org/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 |
URI: | |
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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