8 citations · 28 across the 13 of their papers we have counts for
15 papers
Compatible Relative Lefschetz Fibrations On Admissible Relative Stein Pairs
Yasemin Yildirim, M. Firat Arikan
For more than two decades it has been known that any compact Stein surface (of real dimension four) admits a compatible Lefschetz fibration over a two-disk. More recently, Giroux a…
Compatible Relative Open Books on Relative Contact Pairs via Generalized Square Bridge Diagrams
I. Ozge Taspinar, M. Firat Arikan
Using square bridge position, Akbulut-Ozbagci and later Arikan gave algorithms both of which construct an explicit compatible open book decomposition on a closed contact -manifo…
Maximal Page Crossing Numbers of Legendrian Surfaces in Closed Contact 5-Manifolds
M. Firat Arikan, Ozlem Ersen
We introduce a new Legendrian isotopy invariant for any closed orientable Legendrian surface embedded in a closed contact -manifold which admits an "admissable" ope…
On Legendrian Embbeddings into Open Book Decompositions
Selman Akbulut, M. Firat Arikan
We study Legendrian embeddings of a compact Legendrian submanifold sitting in a closed contact manifold whose contact structure is supported by a (contact) open book $\…
Tight contact structures on hyperbolic three-manifolds
M. Firat Arikan, Merve Secgin
We show the existence of tight contact structures on infinitely many hyperbolic three-manifolds obtained via Dehn surgeries along sections of hyperbolic surface bundles over circle…
Contact Symplectic Fibrations and Fiber Connected Sum
M. Firat Arikan
We consider certain type of fiber bundles with odd dimensional compact contact base, exact symplectic fibers, and the structure group contained in the group of exact symplectomorph…
Legendrian Realization in Convex Lefschetz Fibrations and Convex Stabilizations
Selman Akbulut, M. Firat Arikan
In this paper, we study compact convex Lefschetz fibrations on compact convex symplectic manifolds (i.e., Liouville domains) of dimension which are introduced by Seidel and…
Contact Structures on G_2-Manifolds and Spin 7-Manifolds
M. Firat Arikan, Hyunjoo Cho, Sema Salur
We show that there exist infinitely many pairwise distinct non-closed G_2-manifolds (some of which have holonomy full G_2) such that they admit co-oriented contact structures and h…
Existence of Compatible Contact Structures on -manifolds
M. Firat Arikan, Hyunjoo Cho, Sema Salur
In this paper, we show the existence of (co-oriented) contact structures on certain classes of -manifolds, and that these two structures are compatible in certain ways. Moreov…
Stabilizations via Lefschetz Fibrations and Exact Open Books
Selman Akbulut, M. Firat Arikan
We show that if a contact open book on a -manifold () is induced by a Lefschetz fibration , then there is a one-to-one correspondence betwe…
On the Classification of Planar Contact Structures
M. Firat Arikan, Selahi Durusoy
In this paper, we focus on contact structures supported by planar open book decompositions. We study right-veering diffeomorphisms to keep track of overtwistedness property of cont…
A Note on Lefschetz Fibrations on Compact Stein 4-Manifolds
Selman Akbulut, M. Firat Arikan
Loi-Piergallini and Akbulut-Ozbagci showed that every compact Stein surface admits a Lefschetz fibration over the 2-disk with bounded fibers. In this note we give a more intrinsic…
Lefschetz Fibrations on Compact Stein Manifolds
Selman Akbulut, M. Firat Arikan
Here we prove that up to diffeomorphism every compact Stein manifold W of dimension 2n+2>4 admits a Lefschetz fibration over the two-disk with Stein regular fibers, such that the m…
Planar Contact Structures with Binding Number Three
Mehmet Firat Arikan
In this article, we find the complete list of all contact structures (up to isotopy) on closed three-manifolds which are supported by an open book decomposition having planar pages…
On the support genus of a contact structure
Mehmet Firat Arikan
The algorithm given by Akbulut-Ozbagci constructs an explicit open book decomposition on a contact three-manifold described by a contact surgery on a link in the three-sphere. In t…