22 citations · 101 across the 37 of their papers we have counts for
45 papers
The Gompf -Invariant of Canonical Contact Structures via Legendrian Surgery
Mohan Bhupal, Burak Ozbagci
Let be a minimal connected negative-definite plumbing tree with all vertices of genus zero, and let be the oriented link of the corresponding normal complex surface singu…
Complementary legs and symplectic rational balls
John B. Etnyre, Burak Ozbagci, Bülent Tosun
We show that a small Seifert fibered space with complementary legs does not symplectically bound a rational homology ball for at least one choice of orientation. In the case $e_0\l…
Symplectic rational homology ball fillings of Seifert fibered spaces
John B. Etnyre, Burak Ozbagci, Bülent Tosun
We characterize when some small Seifert fibered spaces can be the convex boundaries of symplectic rational homology balls and give strong restrictions for others to bound such mani…
A characterization of quasipositive two-bridge knots
Burak Ozbagci
We prove a simple necessary and sufficient condition for a two-bridge knot K(p,q) to be quasipositive, based on the continued fraction expansion of p/q. As an application, coupled…
Rational blowdown graphs for symplectic fillings of lens spaces
Mohan Bhupal, Burak Ozbagci
In a previous work, we proved that each minimal symplectic filling of any oriented lens space, viewed as the singularity link of some cyclic quotient singularity and equipped with…
Unbraided wiring diagrams for Stein fillings of lens spaces
Mohan Bhupal, Burak Ozbagci
In a previous work, we constructed a planar Lefschetz fibration on each Stein filling of any lens space equipped with its canonical contact structure. Here we describe an algorithm…
Minimal number of singular fibers in a nonorientable Lefschetz fibration
Sinem Onaran, Burak Ozbagci
We show that there exists an admissible nonorientable genus Lefschetz fibration with only one singular fiber over a closed orientable surface of genus if and only if $g \ge…
Complex vs convex Morse functions and geodesic open books
Pierre Dehornoy, Burak Ozbagci
Suppose that is a closed and oriented surface equipped with a Riemannian metric. In the literature, there are three seemingly distinct constructions of open books on the unit (…
Lefschetz fibrations on nonorientable 4-manifolds
Maggie Miller, Burak Ozbagci
Let be a nonorientable -dimensional handlebody without - and -handles. We show that admits a Lefschetz fibration over the -disk, whose regular fiber is a nonori…
Generalizations of planar contact manifolds to higher dimensions
Bahar Acu, John B. Etnyre, Burak Ozbagci
Iterated planar contact manifolds are a generalization of three dimensional planar contact manifolds to higher dimensions. We study some basic topological properties of iterated pl…
On open books for nonorientable 3-manifolds
Burak Ozbagci
We show that the monodromy of Klassen's genus two open book for is the -homeomorphism of Lickorish, which is also known as the crosscap slide. Similarly, we sho…
Stein and Weinstein structures on disk cotangent bundles of surfaces
Burak Ozbagci
In 1998, Gompf described a Stein domain structure on the disk cotangent bundle of any closed surface S, by a Legendrian handlebody diagram. We prove that Gompf's Stein domain is sy…
Genus one Lefschetz fibrations on disk cotangent bundles of surfaces
Burak Ozbagci
We describe a Lefschetz fibration of genus one on the disk cotangent bundle of any closed orientable surface S. As a corollary, we obtain an explicit genus one open book decomposit…
Trisections of 4-manifolds via Lefschetz fibrations
Nickolas A. Castro, Burak Ozbagci
We develop a technique for gluing relative trisection diagrams of -manifolds with nonempty connected boundary to obtain trisection diagrams for closed -manifolds. As an appli…
Fillings of unit cotangent bundles of nonorientable surfaces
Youlin Li, Burak Ozbagci
We prove that any minimal weak symplectic filling of the canonical contact structure on the unit cotangent bundle of a nonorientable closed surface other than the real projective p…
Canonical contact unit cotangent bundle
Takahiro Oba, Burak Ozbagci
We describe an explicit open book decomposition adapted to the canonical contact structure on the unit cotangent bundle of a compact surface.
Contact open books with exotic pages
Burak Ozbagci, Otto van Koert
We consider a fixed contact 3-manifold that admits infinitely many compact Stein fillings which are all homeomorphic but pairwise non-diffeomorphic. Each of these fillings gives ri…
Generalized plumbings and Murasugi sums
Burak Ozbagci, Patrick Popescu-Pampu
We propose a generalization of the classical notions of plumbing and Murasugi summing operations to smooth manifolds of arbitrary dimensions, so that in this general context Gabai'…
Symplectic fillings of lens spaces as Lefschetz fibrations
Mohan Bhupal, Burak Ozbagci
We construct a positive allowable Lefschetz fibration over the disk on any minimal weak symplectic filling of the canonical contact structure on a lens space. Using this constructi…
Exotic Stein fillings with arbitrary fundamental group
Anar Akhmedov, Burak Ozbagci
For any finitely presentable group , we show the existence of an isolated complex surface singularity link which admits infinitely many exotic Stein fillings such that the funda…
Canonical contact structures on some singularity links
Mohan Bhupal, Burak Ozbagci
We identify the canonical contact structure on the link of a simple elliptic or cusp singularity by drawing a Legendrian handlebody diagram of one of its Stein fillings. We also sh…
Singularity links with exotic Stein fillings
Anar Akhmedov, Burak Ozbagci
In a recent paper of Akhmedov, Etnyre, Mark and Smith, it was shown that there exist infinitely many contact Seifert fibered 3-manifolds each of which admits infinitely many exotic…
On the Heegaard genus of contact 3-manifolds
Burak Ozbagci
It is well-known that Heegaard genus is additive under connected sum of 3-manifolds. We show that Heegaard genus of contact 3-manifolds is not necessarily additive under contact co…
Milnor fillable contact structures are universally tight
Yanki Lekili, Burak Ozbagci
We show that the canonical contact structure on the link of a normal complex singularity is universally tight. As a corollary we show the existence of closed, oriented, atoroidal 3…