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
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:	Publisher
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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