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

Andrea Loi; Riccardo Piergallini

doi:10.1007/s002220000106

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

Andrea Loi·Riccardo Piergallini

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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.

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Andrea Loi, Riccardo Piergallini. 2000-02-07. Compact Stein surfaces with boundary as branched covers of $\B^4$. https://doi.org/10.1007/s002220000106

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