On the universal cover and the fundamental group of an RCD*(K,N)-space

Abstract

Abstract The main goal of the paper is to prove the existence of the universal cover for 𝖱𝖢𝖣 * ⁢ ( K , N ) {\mathsf{RCD}^{*}(K,N)} -spaces. This generalizes earlier work of [43, 44] on the existence of universal covers for Ricci limit spaces. As a result, we also obtain several structure results on the (revised) fundamental group of 𝖱𝖢𝖣 * ⁢ ( K , N ) {\mathsf{RCD}^{*}(K,N)} -spaces. These are the first topological results for 𝖱𝖢𝖣 * ⁢ ( K , N ) {\mathsf{RCD}^{*}(K,N)} -spaces without extra structural-topological assumptions (such as semi-local simple connectedness).