The Milnor-fiber equivalence conjecture for central arrangements

Let ${\mathcal{A}}$ and ${\mathcal{A}}'$ be central arrangements in $\mathbb{C}^3$, let $F({\mathcal{A}})$ denote the Milnor fiber, and let ${\partial{{\overline{F}}}}({\mathcal{A}})$ denote its boundary manifold. Let $L({\mathcal{A}})$ be the intersection lattice. Milnor-fiber equivalence conjecture. The following conditions are equivalent: $F({\mathcal{A}})\cong F({\mathcal{A}}')$; ${\partial{{\overline{F}}}}({\mathcal{A}})\simeq {\partial{{\overline{F}}}}({\mathcal{A}}')$; and $L({\mathcal{A}})\cong L({\mathcal{A}}')$.

This is proposed as a Milnor-fiber analogue of the preceding arrangement-complement conjecture. The source exhibits arrangements with identical homological monodromy data but non-isomorphic Milnor-fiber fundamental groups, and gives no resolution of the equivalence above.