Zoom link: https://princeton.zoom.us/j/594605776

We prove that manifolds with $\lceil n/2 \rceil$-positive curvature operators are rational homology spheres. This is a consequence of a general vanishing and estimation theorem for the $p$-th Betti number for manifolds with a lower bound on the average of the lowest $(n-p)$ eigenvalues of the curvature operator. Our main tool is the Bochner Technique. We will also discuss similar results for the Hodge numbers of Kaehler manifolds.

This talk is based on joint work with Peter Petersen.