Mondino’s orbifold conjecture for noncollapsed RCD(−2,3) spaces

Establish that every noncollapsed RCD(−2,3) metric measure space (X,d,H^3) is homeomorphic to a three-dimensional orbifold, possibly with boundary; equivalently, show that the local topology is determined by the topology of tangent cones.

Background

Within the RCD framework, tangent cone cross-sections of noncollapsed RCD(K,n) spaces are again noncollapsed RCD spaces. For three-dimensional RCD spaces, the authors prove a manifold recognition theorem (Theorem 1.8) in the special case when all tangent cone cross-sections are S^2, but the general orbifold characterization remains conjectural.

A resolution would give a complete topological description of noncollapsed RCD(−2,3) spaces, paralleling the classical Alexandrov theory where local topology is tightly controlled by tangent cone geometry.