Topological invariance of complete integrability for foliations by curves

Let $\mathcal{F}_1$ and $\mathcal{F}_2$ be foliations by curves on $(\mathbb{C}^3,0)$. Suppose they are topologically equivalent and do not admit invariant surfaces over which the induced foliations are dicritical. Topological invariance conjecture. The foliation $\mathcal{F}_1$ admits two holomorphic first integrals if and only if $\mathcal{F}_2$ does. This proposes that, after excluding invariant surfaces supporting dicritical induced foliations, the existence of two independent holomorphic first integrals is a topological invariant; the source presents it as a conjectural generalization in the setting of completely integrable foliations.