Collapsing with a lower curvature bound and \hat{A}-genus

Vitali Kapovitch, University of California, Santa Barbara

Abstract: We show that a simply connected spin 4-manifold which can collapse with curvature bounded below and diameter above satisfies |\hat{A}|\le 2. This provides a partial answer to a question of Petrunin and Lott of whether any spin manifold that can collapse with curvature bounded below and diameter above has $\hat{A}=0$. No prior knowledge of the subjects involved is required.