Compact Stein surfaces with boundary as branched covers of B4

By Andrea Loi, Riccardo Piergallini. 2000

163 citations recorded by the source corpus.

Abstract.We prove that Stein surfaces with boundary coincide up to orientation preserving diffeomorphisms with simple branched coverings of B4 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/00d25b07a0225e18d703b4a8c4027cf3fd351bc4

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Cabling, contact structures and mapping class monoids (2010, background): “ultiplication map in Heegaard Floer homology. (We note that the comultiplication map can be deﬁned using our Theorem 1.3). The other three monoids were previously unknown. It has long been known, cf. [1, 41], that monodromies in Dehn+(Σ), the monoid generated by all righthanded Dehn twists on Σ, giv”
Contact 3-manifolds with infinitely many Stein fillings (2003, result): “We only sketch the proof of the above theorem, since it was already proved in [ 14 ], [3] (with the extra assumption of having only homologically essential vanishing cycles in the bration), and also appeared in [7].”
Right-veering diffeomorphisms of compact surfaces with boundary (2005, background): “In the framework of open book decompositions, the holomorphically fillable contact structures admit a simple characterization, as a result of work by Loi–Piergallini [ LP ], combined with the relative version of the above theorem.”
Few remarks about symplectic filling (2003, background): “The equivalence between (Stein-2) and (Stein-3) is established in [1] and [24].”
Lefschetz fibrations on compact Stein surfaces (2000, methodology): “The existence of a positive allowable Lefschetz bration on a compact Stein surface with boundary was established by Loi and Piergallini [10] using branched covering techniques.”
On the topology of compact Stein surfaces (2001, background): “In [AO] (see also [ LP ]), it was proved that every compact Stein surface admits a”
Brieskorn manifolds in contact topology (2013, background): “ealized by Loi-Piergallini that Stein-llable contact 3-manifolds admit open books with a special monodromy, namely the product of right-handed Dehn twists, BRIESKORN MANIFOLDS IN CONTACT TOPOLOGY 17 [LP]. We will explain the notions of monodromy and Dehn twists below in more detail. Giroux brought o”
Reeb vector fields and open book decompositions (2008, background): “Akbulut-Ozbagci [AO] and Giroux (independently) also clarified the role of Stein fillability, inspired by the work of Loi-Piergallini [ LP ]:”