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 application we give infinitely many examples of overtwisted contact structures supported by open books whose pages are the four-punctured sphere, and also we prove that a certain family is Stein fillable using lantern relation.


On the arc and curve complex of a surface
Korkmaz, Mustafa (Cambridge University Press (CUP), 2010-05-01)
We study the arc and curve complex AC(S) of an oriented connected surface S of finite type with punctures. We show that if the surface is not a sphere with one, two or three punctures nor a torus with one puncture, then the simplicial automorphism group of AC(S) coincides with the natural image of the extended mapping class group of S in that group. We also show that for any vertex of AC(S), the combinatorial structure of the link of that vertex characterizes the type of a curve or of an arc in S that repre...
On symplectic quotients of K3 surfaces
Cinkir, Z; Onsiper, H (Elsevier BV, 2000-12-18)
In this note, we construct generalized Shioda-Inose structures on K3 surfaces using cyclic covers and almost functoriality of Shioda-Inose structures with respect to normal subgroups of a given group of symplectic automorphisms.
On the Krall-type polynomials on q-quadratic lattices
Alvarez-Nodarse, R.; Adiguzel, R. Sevinik (Elsevier BV, 2011-08-01)
In this paper, we study the Krall-type polynomials on non-uniform lattices. For these polynomials the second order linear difference equation, q-basic series representation and three-term recurrence relations are obtained. In particular, the q-Racah-Krall polynomials obtained via the addition of two mass points to the weight function of the non-standard q-Racah polynomials at the ends of the interval of orthogonality are considered in detail. Some important limit cases are also discussed. (C) 2011 Royal Net...
Invariants of Legendrian Knots from Open Book Decompositions
Onaran, Sinem Celik (Oxford University Press (OUP), 2010-01-01)
In this note, we define a new invariant of a Legendrian knot in a contact 3-manifold using an open book decomposition supporting the contact structure. We define the support genus sg(L) of a Legendrian knot L in a contact 3-manifold (M, xi) as the minimal genus of a page of an open book of M supporting the contact structure xi such that L sits on a page and the framings given by the contact structure and the page agree. We show that any null-homologous loose knot in an overtwisted contact structure has supp...
On Legendrian embbeddings into open book decompositions
Akbulut, Selman; Arikan, M. Firat (International Press of Boston, 2019-01-01)
We study Legendrian embeddings of a compact Legendrian submanifold L sitting in a closed contact manifold (M, xi) whose contact structure is supported by a (contact) open book OB on M. We prove that if OB has Weinstein pages, then there exist a contact structure xi' on M, isotopic to xi and supported by OB, and a contactomorphism f:(M, xi) -> (M, xi') such that the image f(L) of any such submanifold can be Legendrian isotoped so that it becomes disjoint from the closure of a page of OB.
Citation Formats
M. F. Arıkan, “ON THE CLASSIFICATION OF CERTAIN PLANAR CONTACT STRUCTURES,” ACTA MATHEMATICA HUNGARICA, pp. 529–542, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34400.