Department of Mathematics
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Contact Symplectic Fibrations and Bundle Contact Structures
Arıkan, Mehmet Fırat (2023-12-01)
We consider a certain type of fiber bundles with odd dimensional connected contact base, exact symplectic fibers, and the structure group contained in the group of exact symplectomorphisms of the fiber. We call such fibrat...
Tight contact structures on hyperbolic three-manifolds
Arıkan, Mehmet Fırat (Elsevier BV, 2017-11-01)
Let Sigma(g) denote a closed orientable surface of genus g >= 2. We consider a certain infinite family of Sigma(g)-bundles over circle whose monodromies are taken from some collection of pseudo-Anosov diffeomorphisms. We s...
Stabilizations via Lefschetz fibrations and exact open books
Arıkan, Mehmet Fırat (2017-01-01)
We show that if a contact open book (Σ, h) on a (2n + 1)-manifold M (n ≥ 1) is induced by a Lefschetz fibration π : W → D2 , then there is a 1-1 correspondence between positive stabilizations of (Σ, h) and positive stabili...
Legendrian realization in convex Lefschetz fibrations and convex stabilizations
Akbulut, Selman; Arıkan, Mehmet Fırat (Walter de Gruyter GmbH, 2015-05-01)
We show that, up to a Liouville homotopy and a deformation of compact convex Lefschetz fibrations on W, any Lagrangian submanifold with trivial first de Rham cohomology group, embedded on a (symplectic) page of the (induce...
Arıkan, Mehmet Fırat; Salur, Sema (International Press of Boston, 2013-06-01)
In this paper, we show the existence of (co-oriented) contact structures on certain classes of G(2)-manifolds, and that these two structures are compatible in certain ways. Moreover, we prove that any seven-manifold with a...
A note on Lefschetz fibrations on compact Stein 4-manifolds
Arikan, M. Firat; Arıkan, Mehmet Fırat (2012-10-01)
Loi-Piergallini and Akbulut-Ozbagci showed that every compact Stein surface admits a Lefschetz fibration over the disk D-2 with bounded fibers. In this note we give a more intrinsic alternative proof of this result.
A normally closed electrostatic parylene microvalve for micro total analysis systems
Yıldırım, Ender; Arıkan, Mehmet Fırat; Külah, Haluk (2012-07-01)
This paper presents an electrostatically actuated, normally closed microvalve for parylene microfluidics. The proposed valve structure isolates the fluid from the electric field, and hence results in relatively low actuati...
Arıkan, Mehmet Fırat (Springer Science and Business Media LLC, 2012-03-01)
We focus on contact structures supported by planar open book decompositions. We study right-veering diffeomorphisms to keep track of overtwistedness property of contact structures under some monodromy changes. As an applic...
Evaluation of selected kaolins as raw materials for the Turkish cement and concrete industry
Aras, A.; Albayrak, M.; Arıkan, Mehmet Fırat; Sobolev, K. (Mineralogical Society, 2007-6)
<jats:title>Abstract</jats:title><jats:p>Turkey has a long tradition (starting with prehistoric civilizations) and experience in exploring for raw clay materials and processing them into ceramic products. Many of these pro...
Planar Contact Structures with Binding Number Three
Arıkan, Mehmet Fırat (2007-01-01)
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 with three (but not less) boundary compon...
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