Let we  have a 3 manifold  $M$ with a  codimension 1 foliation tangent to $\alpha=0$ for  a  1  form $\alpha$. Then $\alpha \wedge d\alpha =0$  then  $\exists \beta $ with $d\alpha =\alpha \wedge \beta$. The  Godbilon Vey invariant is  defined as cohomology class of  $\beta \wedge d\beta$.

The  conjecture about this  invariant is that it is a topological invariant.

>What are some updates on this  conjecture?