#### Volume 25, issue 1 (2021)

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On the topology and the boundary of $N$–dimensional $\mathsf{RCD}(K,N)$ spaces

### Vitali Kapovitch and Andrea Mondino

Geometry & Topology 25 (2021) 445–495
##### Abstract

We establish topological regularity and stability of $N$–dimensional $\mathsf{RCD}\left(K,N\right)$ spaces (up to a small singular set), also called noncollapsed $\mathsf{RCD}\left(K,N\right)$ 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.

##### Keywords
Ricci curvature, optimal transport, metric measure spaces
Primary: 53C23
Secondary: 53C21
##### Publication
Received: 15 August 2019
Revised: 29 February 2020
Accepted: 31 March 2020
Published: 2 March 2021
Proposed: Tobias H Colding
Seconded: David M Fisher, Bruce Kleiner
##### Authors
 Vitali Kapovitch Department of Mathematics University of Toronto Toronto, ON Canada Andrea Mondino Mathematical Institute University of Oxford Oxford United Kingdom