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    Intermediate curvatures and highly connected manifolds

    Crowley, Diarmuid and Wraith, David (2022) Intermediate curvatures and highly connected manifolds. Asian Journal of Mathematics, 26 (3). pp. 407-454. ISSN 1093-6106

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    We show that after forming a connected sum with a homotopy sphere, all (2j-1)-connected 2j-parallelisable manifolds in dimension 4j+1, j > 0, can be equipped with Riemannian metrics of 2-positive Ricci curvature. When j=1 we extend the above to certain classes of simply-connected non-spin 5-manifolds. The condition of 2-positive Ricci curvature is defined to mean that the sum of the two smallest eigenvalues of the Ricci tensor is positive at every point. This result is a counterpart to a previous result of the authors concerning the existence of positive Ricci curvature on highly connected manifolds in dimensions 4j-1 for j > 1, and in dimensions 4j+1 for j > 0 with torsion-free cohomology. A key technical innovation involves performing surgery on links of spheres within 2-positive Ricci curvature.

    Item Type: Article
    Keywords: Intermediate curvatures; highly connected; manifolds;
    Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
    Item ID: 18507
    Identification Number:
    Depositing User: Dr. David Wraith
    Date Deposited: 14 May 2024 11:11
    Journal or Publication Title: Asian Journal of Mathematics
    Publisher: International Press
    Refereed: Yes
    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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