Conjecture that all Lagrangian homology classes of simply connected Calabi–Yau manifolds lie in ${\mathcal S}$

Let $N$ be a simply connected closed Calabi–Yau manifold of any complex dimension, and let ${\mathcal S}$ denote the subgroup generated by special Lagrangian cycles. Lagrangian homology generation conjecture. All Lagrangian homology classes of $N$ lie in ${\mathcal S}$. The paper establishes results in low dimensions and describes this assertion as reasonable; the claim in arbitrary complex dimension remains open.