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    Intermediate Ricci Curvatures and Gromov’s Betti number bound


    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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