Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4657715 | Topology | 2006 | 17 Pages |
Abstract
We say that an oriented contact manifold (M,ξ)(M,ξ) is Milnor fillable if it is contactomorphic to the contact boundary of an isolated complex-analytic singularity (X,x)(X,x). 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 f:(X,x)→(C,0)f:(X,x)→(C,0), with isolated singularity at x and we verify that all these open books carry the contact structure ξξ of (M,ξ)(M,ξ)—generalizing results of Milnor and Giroux.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Clément Caubel, András Némethi, Patrick Popescu-Pampu,