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

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

2000-02-07

arxiv.org/abs/math/0002042v1

Mathematics

Geometric Topology

25 pages, 20 postscript figures. LaTeX file. Uses: geom.sty epsf.sty

Scientific paper

10.1007/s002220000106

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.

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