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

Abstract

We prove that Stein surfaces with boundary coincide up to orientation preserving diffeomorphisms with simple branched coverings of \B^4 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.Comment: 25 pages, 20 postscript figures. LaTeX file. Uses: geom.sty epsf.st