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Ricci-limit nature of Z in (n−3)-symmetric noncollapsed Ricci limits for n ≥ 4

Determine whether, for n ≥ 4, the metric space Z arising in the decomposition (X,d) = R^{n−3} × Z of a noncollapsed Ricci limit space is itself a noncollapsed three-dimensional Ricci limit space.

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Background

Theorem 1.7 shows Z is a topological 3-manifold when X decomposes isometrically as R{n−3} × Z. However, whether Z inherits the structure of a noncollapsed 3D Ricci limit space is unknown in higher ambient dimensions.

Resolving this would clarify the internal structure of symmetric strata and the behavior of cross-sections under noncollapsed limits.

References

Moreover, it is presently an open question whether any metric space (Z ,d ) aZ in the statement of Theorem 1.7 is a noncollapsed three-dimensional Ricci limit space when n ≥ 4.

— Topological regularity and stability of noncollapsed spaces with Ricci curvature bounded below (2405.03839 - Bruè et al., 6 May 2024) in Section 1.3 (The topology of three-dimensional RCD spaces)