Compact Stein surfaces with boundary as branched covers of B^4

LOI, ANDREA;PIERGALLINI R.

2001-01-01

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Abstract

WeprovethatSteinsurfaceswithboundarycoincideuptoorien- tation preserving diffeomorphisms with simple branched coverings of B4 whose branch set is a positive braided surface. As a consequence, we have that a smooth oriented 3-manifold is Stein fillable iff it has a positive open- book decomposition.