On the topology and the boundary of N-dimensional RCD(K,N) spaces

Abstract

We establish topological regularity and stability of N-dimensional RCD(K,N) spaces (up to a small singular set), also called non-collapsed RCD(K,N) in the literature. We also introduce the notion of a boundary of such spaces and study its properties, including its behavior under Gromov-Hausdorff convergence.

32 pages. Final version to appear in "Geometry & Topology"