Reiser, Philipp Wraith, David J. 2023-09-20 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. application/pdf https://folia.unifr.ch/global/documents/326114 https://folia.unifr.ch/documents/326114/files/reiser-wraith_intermediatericcicurvaturesandgromovsbettinumberbound.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s12220-023-01423-6 info:eu-repo/semantics/altIdentifier/issn/1050-6926 info:eu-repo/semantics/openAccess CC BY The Journal of Geometric Analysis. - Springer Science and Business Media LLC. - 2023, vol. 33, no. 12 Riemannian geometry Intermediate Ricci curvatures Surgery Total Betti numbers info:eu-repo/classification/udc/51 Intermediate Ricci Curvatures and Gromov’s Betti number bound http://purl.org/coar/resource_type/c_6501