Milnor open books and Milnor fillable contact 3-manifolds (Q2488875)

A construction of \textit{A. N. Varchenko} [Mosc. Univ. Math. Bull. 35, No. 2, 18--22 (1980); translation from Vestn. Mosk. Univ., Ser. I 1980, No. 2, 18--21 (1980; Zbl 0453.53027)] associates with an irreducible germ \((X,x)\) of a complex analytic variety, which is smooth outside \(x\), an oriented real compact contact manifold; such a contact manifold is called Milnor fillable. The main theorem of the paper asserts that any Milnor fillable 3-manifold admits a unique Milnor fillable contact structure up to isomorphy. The proof is based on the connection between the Milnor fillable contact structures and the so-called open book decompositions.