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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Abstract

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:	https://doi.org/10.4310/ajm.2022.v26.n3.a3
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
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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