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

created by mondino on 10 May 2016
modified on 14 Sep 2016

[BibTeX]

Journal für die reine und angewandte mathematik

Inserted: 10 may 2016
Last Updated: 14 sep 2016

Year: 2016

Abstract:

The main goal of the paper is to prove the existence of the universal cover for $RCD^*(K,N)$-spaces. This generalizes earlier work of C. Sormani and the second author 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 $RCD^*(K,N)$-spaces. These are the first topological results for $RCD^{*}(K,N)$-spaces without extra structural-topological assumptions (such as semi-local simple connectedness).