Milnor open books and Milnor fillable contact 3-manifolds

• Autores: Clément Caubel, András Némethi, Patrick Popescu-Pampu
• Localización: Topology, ISSN 0040-9383, Vol. 45, Nº 3, 2006, pág. 673
• Idioma: inglés
• DOI: 10.1016/j.top.2006.01.002
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• Resumen

  • 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.