Some new obstruction results for compact positively Ricci curved manifolds

Abstract

This work considers the fundamental groups and diameters of positively Ricci curved Riemannian $n$-manifolds. By combining the results of equivarient Hausdorff convergence with the Ricci version of a splitting theorem, some new information on the topology of compact manifolds with positive Ricci curvature was discovered. Moreover, a weak Margulis's lemma was also obtained for Riemannian manifolds with a lower Ricci curvature bound.