Yau's conjecture on the topology of isolated surface singularities

Let $(V_i,0)\subset(\mathbb{C}^3,0)$, for $i=1,2$, be germs of isolated surface singularities. Let $K_1,K_2$ be their links, and let $\Delta_1,\Delta_2$ be the characteristic polynomials of their monodromies. Yau's conjecture. If $K_1$ is homeomorphic to $K_2$ and $\Delta_1=\Delta_2$, then $V_1$ and $V_2$ have the same embedded topology: there is a germ of a homeomorphism $\Psi:(\mathbb{C}^3,0)\to(\mathbb{C}^3,0)$ such that $\Psi(V_1)=V_2$. The conjecture asks whether abstract topology together with the monodromy characteristic polynomial determines the embedded topology of an isolated surface singularity.