Intermediate Ricci Curvatures and Gromov’s Betti number bound

Reiser, Philipp; Wraith, David J.

doi:10.1007/s12220-023-01423-6

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Journal article

Intermediate Ricci Curvatures and Gromov’s Betti number bound

DOKPE

Reiser, Philipp ORCID University of Fribourg
Wraith, David J. Maynooth University

20.09.2023

Published in:

The Journal of Geometric Analysis. - Springer Science and Business Media LLC. - 2023, vol. 33, no. 12

English We consider intermediate Ricci curvatures $Ric_k$ 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 $Ric_k>0$, we show that Gromov's upper Betti number bound for sectional curvature bounded below fails to hold for $Ric_k>0$ when $\lfloor n/2 \rfloor+2 \le k \le n-1.$ This was previously known only in the case of positive Ricci curvature.

Faculty

Faculté des sciences et de médecine

Department

Département de Mathématiques

Language