Vitali Kapovitch, University of Toronto

Title: Mixed curvature almost flat manifolds

Abstract: A celebrated theorem of Gromov says that given n > 1 there is an ε=ε(n) > 0 such that if a closed Riemannian manifold Mn satisfies the condition
-ε < secM < ε, and diam(M)< 1, then M is diffeomorphic to an infranilmanifold. I will show that the lower sectional curvature bound in Gromov's theorem can be weakened to the lower Bakry-Emery Ricci curvature bound. I will also discuss the relation of this result to the study of manifolds with Ricci curvature bounded below.