Dear all,

we are pleased to announce the next appointment of the joint UNIPI-SNS Geometric Analysis Seminar.

This week the speaker is Mattia Magnabosco, from University of Oxford.

Tuesday, April 28, 10:00, Aula Seminari - Dipartimento di Matematica - UNIPI

Title: New topological restrictions for spaces with nonnegative Ricci curvature
Abstract: The topology of complete noncompact Riemannian manifolds with nonnegative Ricci curvature has been studied extensively since the earliest developments of Geometric Analysis. In dimension 3, a complete topological classification was only recently achieved by Gang Liu, with a strategy based on minimal surfaces methods. They proved that a 3-dimensional Riemannian manifold with nonnegative Ricci curvature either is homeomorphic to R^3 or the universal cover splits a line isometrically. In this talk, I present an alternative proof of Liu’s classification, which also works for nonsmooth RCD(0,3) spaces. This generalisation of Liu’s theorem yields, as a consequence, the full classification of non-collapsed RCD(0,3) spaces without boundary. Our strategy relies on two main building blocks of independent interest, which provide results that are new also in the smooth setting. In particular, we prove that, given a complete n-dimensional Riemannian manifold (M,g) with nonnegative Ricci curvature and first Betti number b_1(M) ≥ n-2, the universal cover splits R^{n-2} isometrically. Moreover, we show that every complete oriented n-dimensional Riemannian manifold with nonnegative Ricci curvature has vanishing simplicial volume.