Researcher:
Özbağcı, Burak

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Burak

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Özbağcı

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Özbağcı, Burak

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Researcher Of Publications: search.filters.isAuthorOfPublication.40de6999-393c-4978-8ee2-df2e85e835af

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Now showing 1 - 10 of 33
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    Surgery diagrams for horizontal contactstructures
    (Springer, 2008) N/A; Department of Mathematics; Özbağcı, Burak; Faculty Member; Department of Mathematics; College of Sciences; 29746
    We describe Legendrian surgery diagrams for some horizontal contact structures on non-positive plumbing trees of oriented circle bundles over spheres with negative Euler numbers. As an application we determine Millior fillable contact structures on some Milnor fillable 3-manifolds.
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    Exotic stein fillings with arbitrary fundamental group
    (Springer, 2018) Akhmedov, Anar; Department of Mathematics; Özbağcı, Burak; Faculty Member; Department of Mathematics; College of Sciences; 29746
    Let G be a finitely presentable group. We provide an infinite family of homeomorphic but pairwise non-diffeomorphic, symplectic but non-complex closed 4-manifolds with fundamental group G such that each member of the family admits a Lefschetz fibration of the same genus over the two-sphere. As a corollary, we also show the existence of a contact 3-manifold which admits infinitely many homeomorphic but pairwise non-diffeomorphic Stein fillings such that the fundamental group of each filling is isomorphic to G. Moreover, we observe that the contact 3-manifold above is contactomorphic to the link of some isolated complex surface singularity equipped with its canonical contact structure.
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    Contact open books with exotic pages
    (Springer Basel Ag, 2015) van Koert, Otto; Department of Mathematics; Özbağcı, Burak; Faculty Member; Department of Mathematics; College of Sciences; 29746
    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 rise to a closed contact 5-manifold described as a contact open book whose page is the filling at hand and whose monodromy is the identity symplectomorphism. We show that the resulting infinitely many contact 5-manifolds are all diffeomorphic but pairwise non-contactomorphic. Moreover, we explicitly determine these contact 5-manifolds.
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    Explicit horizontal open books on some Seifert fibered 3-manifolds
    (Elsevier Science Bv, 2007) N/A; Department of Mathematics; Özbağcı, Burak; Faculty Member; Department of Mathematics; College of Sciences; 29746
    We describe explicit horizontal open books on some Seifert fibered 3-manifolds. We show that the contact structures compatible with these horizontal open books are Stein fillable and horizontal as well. Moreover we draw surgery diagrams for some of these contact structures.
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    Symplectic fillings of lens spaces as Lefschetz fibrations
    (European Mathematical Society, 2016) Bhupal, M.; Department of Mathematics; Özbağcı, Burak; Faculty Member; Department of Mathematics; College of Sciences; 29746
    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 construction we prove that any minimal symplectic filling of the canonical contact structure on a lens space is obtained by a sequence of rational blowdowns from the minimal resolution of the corresponding complex two-dimensional cyclic quotient singularity.
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    Full lutz twist along the binding of an open book
    (Springer, 2010) N/A; Department of Mathematics; Department of Mathematics; Özbağcı, Burak; Pamuk, Mehmetçik; Faculty Member; Researcher; Department of Mathematics; College of Sciences; College of Sciences; 29746; 163666
    Let T denote a binding component of an open book (Sigma, phi) compatible with a closed contact 3-manifold (M, xi). We describe an explicit open book (Sigma', phi') compatible with (M, zeta), where zeta is the contact structure obtained from xi by performing a full Lutz twist along T. Here, (Sigma', phi') is obtained from (Sigma, phi) by a local modification near the binding.
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    Invariants of contact structures from open books
    (Amer Mathematical Soc, 2008) Etnyre, John B.; Department of Mathematics; Özbağcı, Burak; Faculty Member; Department of Mathematics; College of Sciences; 29746
    In this note we de. ne three invariants of contact structures in terms of open books supporting the contact structures. These invariants are the support genus (which is the minimal genus of a page of a supporting open book for the contact structure), the binding number (which is the minimal number of binding components of a supporting open book for the contact structure with minimal genus pages) and the norm (which is minus the maximal Euler characteristic of a page of a supporting open book).
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    Embedding fillings of contact 3-manifolds
    (Elsevier Gmbh, 2006) N/A; Department of Mathematics; Özbağcı, Burak; Faculty Member; Department of Mathematics; College of Sciences; 29746
    In this survey article, we describe different ways of embedding fillings of contact 3-manifolds into closed symplectic 4-manifolds.
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    On the relative Giroux correspondence
    (Amer Mathematical Soc, 2011) Department of Mathematics; Department of Mathematics; Etgü, Tolga; Özbağcı, Burak; Faculty Member; Faculty Member; Department of Mathematics; College of Sciences; College of Sciences; 16206; 29746
    Recently, Honda, Kazez and Matic described an adapted partial open book decomposition of a compact contact 3-manifold with convex boundary by generalizing the work of Giroux in the closed case. They also implicitly established a one-to-one correspondence between isomorphism classes of partial open book decompositions modulo positive stabilization and isomorphism classes of compact contact 3-manifolds with convex boundary. In this expository article we explicate the relative version of Giroux correspondence.
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    Canonical contact unit cotangent bundle
    (Walter De Gruyter Gmbh, 2018) Oba, Takahiro; Department of Mathematics; Özbağcı, Burak; Faculty Member; Department of Mathematics; College of Sciences; 29746
    We describe an explicit open book decomposition adapted to the canonical contact structure on the unit cotangent bundle of a closed surface.