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.

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

Cited by in corpus (24)

• Right-veering diffeomorphisms of compact surfaces with boundary II
• Brieskorn manifolds in contact topology
• Strongly Fillable Contact Manifolds and J-holomorphic Foliations
• Constructing Lefschetz-type fibrations on four-manifolds
• Overtwisted open books from sobering arcs
• Multisections of Lefschetz fibrations and topology of symplectic 4-manifolds
• Kahler decomposition of 4-manifolds
• Stein fillings and SU(2) representations
• Stein fillable Seifert fibered 3-manifolds
• Open books and configurations of symplectic surfaces and erratum
• Positive factorizations of mapping classes
• Fillings of unit cotangent bundles of nonorientable surfaces
• Floer theory of higher rank quiver 3-folds
• Braiding link cobordisms and non-ribbon surfaces
• Lefschetz pencils and finitely presented groups
• Factorizations of diffeomorphisms of compact surfaces with boundary
• Stein fillable contact 3-manifolds and positive open books of genus one
• Singular maps on exotic 4-manifold pairs
• A real open book not fillable by a real Lefschetz fibration
• Universal Lefschetz fibrations over bounded surfaces
• Compact Stein surfaces as branched covers with same branch sets
• Universal Lefschetz fibrations and Lefschetz cobordisms
• Representing Dehn twists with branched coverings
• Positive factorizations of pseudoperiodic homeomorphisms