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- Title
Intermediate Ricci Curvatures and Gromov's Betti number bound.
- Authors
Reiser, Philipp; Wraith, David J.
- Abstract
We consider intermediate Ricci curvatures R i c k on a closed Riemannian manifold M n . 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 R i c k > 0 , we show that Gromov's upper Betti number bound for sectional curvature bounded below fails to hold for R i c k > 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).
- Subjects
BETTI numbers; CURVATURE; RIEMANNIAN manifolds; RIEMANNIAN geometry
- Publication
Journal of Geometric Analysis, 2023, Vol 33, Issue 12, p1
- ISSN
1050-6926
- Publication type
Article
- DOI
10.1007/s12220-023-01423-6