Matthias Wink, UCLA

Title: Vanishing and Estimation Results for Betti numbers

Abstract: We prove that manifolds with ⌈ n/2 ⌉-positive
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. Time permitting, we will also discuss similar
results for the Hodge numbers of Kähler manifolds. This talk
is based on joint work with Peter Petersen.