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

Authors
Loi, A Piergallini, R
Citation
A. Loi et R. Piergallini, Compact Stein surfaces with boundary as branched covers of B-4, INVENT MATH, 143(2), 2001, pp. 325-348
Citations number
36
Categorie Soggetti
Mathematics
Journal title
INVENTIONES MATHEMATICAE
ISSN journal
00209910 → ACNP
Volume
143
Issue
2
Year of publication
2001
Pages
325 - 348
Database
ISI
SICI code
0020-9910(200102)143:2<325:CSSWBA>2.0.ZU;2-I
Abstract
We prove that Stein surfaces with boundary coincide up to orientation prese rving diffeomorphisms with simple branched coverings of B-4 whose branch se t is a positive braided surface. As a consequence, we have that a smooth or iented 3-manifold is Stein fillable iff it has a positive open-book decompo sition.