New topological restrictions for complete manifolds with nonnegative Ricci curvature

The classification of complete 3-manifolds with nonnegative Ricci curvature had been an open problem since the early 1980s and it was finally settled by G. Liu in 2011 using minimal surfaces methods. In this talk I will discuss a new approach to this classification problem, based on two results of independent interest that hold in any dimension: a sharp rigidity theorem for the first Betti number and a vanishing theorem for the simplicial volume. Based on joint work with Alessandro Cucinotta and Mattia Magnabosco.