Molino's conjecture on closures of leaves of singular Riemannian foliations

Let $(M,\mathcal{F})$ be a singular Riemannian foliation. The partition $\overline{\mathcal{F}}$ whose elements are the closures of the leaves of $\mathcal{F}$ is defined by

$$\overline{\mathcal{F}}=\{\overline{L}:L\text{ is a leaf of }\mathcal{F}\}.$$

Molino's conjecture. The partition $\overline{\mathcal{F}}$ given by the closures of the leaves of $\mathcal{F}$ is again a singular Riemannian foliation.

The conjecture concerns whether leaf closures inherit the geometric structure of the original singular Riemannian foliation. The paper explains that understanding smooth lifts of flows on local leaf spaces may help establish the conjecture in important cases; no resolution is supplied here.