Embedding fillings of contact 3-manifolds
In this survey article we describe different ways of embedding fillings of contact 3-manifolds into closed symplectic 4-manifolds.
math.SG↗
arXiv subjects
Burak Ozbagci
Publications and source records attributed to Burak Ozbagci.
An open book decomposition compatible with rational contact surgery
We construct an open book decomposition compatible with a contact structure given by a rational contact surgery on a Legendrian link in the standard contact $S^3$. As an application we show that some rational contact surgeries on certain Legendrian knots induce overtwisted contact structures.
math.GT↗
Contact 3-manifolds with infinitely many Stein fillings
Infinitely many contact 3-manifolds each admitting infinitely many, pairwise non-diffeomorphic Stein fillings are constructed. We use Lefschetz fibrations in our constructions and compute their first homologies to distinguish the fillings.
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Lefschetz fibrations on compact Stein surfaces
The existence of a positive allowable Lefschetz fibration on a compact Stein surface with boundary was established by Loi and Piergallini by using branched covering techniques. Here we give an alternative simple proof of this fact and construct explicitly the vanishing cycles of the Lefschetz fibration, obtaining a direct identification of the set of compact Stein manifolds with positive allowable Lefschetz fibrations over a 2-disk. In the process we associate to every compact Stein manifold infinitely many nonequivalent such Lefschetz fibrations.
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On the topology of compact Stein surfaces
In this paper we obtain the following results: (1) Any compact Stein surface with boundary embeds naturally into a symplectic Lefschetz fibration over the 2-sphere. (2) There exists a minimal elliptic fibration over the 2-disk, which is not Stein. (3) The circle bundle over a genus n>1 surface with euler number e=-1 admits at least n+1 mutually non-homeomorphic simply-connected Stein fillings. (4) Any surface bundle over the circle, whose fiber is a closed surface of genus n>0 can be embedded into a closed symplectic 4-manifold, splitting the symplectic 4-manifold into two pieces both of which have positive b_2^+. (5) Every closed, oriented connected 3-manifold has a weakly symplectically fillable double cover, branched along a 2-component link.
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Minimal number of singular fibers in a Lefschetz fibration
There exists a (relatively minimal) genus g Lefschetz fibration with only one singular fiber over a closed (Riemann) surface of genus h iff g>2 and h>1. The singular fiber can be chosen to be reducible or irreducible. Other results are that every Dehn twist on a closed surface of genus at least three is a product of two commutators and no Dehn twist on any closed surface is equal to a single commutator.
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Noncomplex smooth 4-manifolds with genus-2 Lefschetz fibrations
We construct noncomplex smooth 4-manifolds which admit genus-2 Lefschetz fibrations over S^2. The fibrations are necessarily hyperelliptic, and the resulting 4-manifolds are not even homotopy equivalent to complex surfaces. Furthermore, these examples show that fiber sums of holomorphic Lefschetz fibrations do not necessarily admit complex structures.
math.GT↗
Signatures of Lefschetz fibrations
Let M be a smooth 4-manifold which admits a genus g Lefschetz fibration over D^2 or S^2. We develop a technique to compute the signature of M using the global monodromy of this fibration.
math.GT↗