Closure of singular foliations: the proof of Molino's conjecture

TL;DR

This paper proves Molino's conjecture that the closure of leaves in any singular Riemannian foliation forms a new singular Riemannian foliation, confirming a fundamental structural property of such foliations.

Contribution

The paper provides a rigorous proof of Molino's conjecture, establishing that leaf closures preserve the singular Riemannian foliation structure.

Findings

Confirmed that leaf closures form a singular Riemannian foliation

Validated Molino's conjecture for all singular Riemannian foliations

Strengthened understanding of foliation closure properties

Abstract

In this paper we prove the conjecture of Molino that for every singular Riemannian foliation $(M,\mathcal{F})$, the partition $\bar{\mathcal{F}}$ given by the closures of the leaves of $\mathcal{F}$ is again a singular Riemannian foliation.