Lefschetz fibrations on compact Stein surfaces

By S. Akbulut, Burak Ozbagci. 2000

149 citations recorded by the source corpus.

Let M be a compact Stein surface with boundary. We show that M admits infinitely many nonequivalent positive allowable Lefschetz fibrations over D 2 with bounded fibers.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fbbdba5d678f4af7f6bb5ab494231bf234ddeff2

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

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]:”
Planar open books, monodromy factorizations and symplectic fillings (2009, unknown): “Y; /, then X has a structure of an allowable Lefschetz fibration by Akbulut and Ozbagci [1].”
Strongly fillable contact manifolds and $J$-holomorphic foliations (2008, background): “[GS99, AO01 ]) that ( c , ˆ ω) admits a Stein structure.”
On symplectic cobordisms (2001, background): “The following lemma (and more importantly its converse) is due to the efforts of many people,beginning with the work of Loi and Piergallini [23] (also see [25] for an earlier effort),and recently culminating in the work of Giroux [16] (see also [ 3 ] [24]).”
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. (Also see [ AO ].)”
Contact surgeries and the transverse invariant in knot Floer homology (2008, background): “If µ denotes a meridian for C, then we can think of f + µ as a new framing.”
On the topology of compact Stein surfaces (2001, background): “Next we show that the result in [ AO ] does not necessarily hold if the flber of the”
Few remarks about symplectic filling (2003, background): “The equivalence between (Stein-2) and (Stein-3) is established in [1] and [24].”
Cabling, contact structures and mapping class monoids (2010, background): “[1, 41], that monodromies in Dehn(Σ), the monoid generated by all righthanded Dehn twists on Σ, give rise to Stein fillable contact structures and so Dehn(Σ) ⊂ Stein(Σ).”
Contact Structures with Distinct Heegaard Floer Invariants (2003, background): “If X is symplectic, this invariant satisfies an important non-vanishing theorem [OS6].”