Milnor open books and Milnor fillable contact 3-manifolds.(English)Zbl 1098.53064

A construction of 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.

MSC:

 53D35 Global theory of symplectic and contact manifolds 32S55 Milnor fibration; relations with knot theory 57R17 Symplectic and contact topology in high or arbitrary dimension

Zbl 0453.53027
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