Resumen de Milnor open books and Milnor fillable contact 3-manifolds

Clément Caubel, András Némethi, Patrick Popescu-Pampu

• We say that an oriented contact manifold (M,?) is Milnor fillable if it is contactomorphic to the contact boundary of an isolated complex-analytic singularity . In this article we prove that any three-dimensional oriented manifold admits at most one Milnor fillable contact structure up to contactomorphism. The proof is based on Milnor open books: we associate an open book decomposition of M with any holomorphic function , with isolated singularity at x and we verify that all these open books carry the contact structure ? of (M,?)¿generalizing results of Milnor and Giroux.