Researcher:
Etgü, Tolga

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Tolga

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Etgü

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Etgü, Tolga

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2005 - 2009112010 - 20198

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Researcher Of Publications: search.filters.isAuthorOfPublication.4cb8325c-8131-46cc-b7e7-76107d9c56a3

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Now showing 1 - 10 of 19
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    Symplectic and Lagrangian surfaces in 4-manifolds
    (Rocky Mt Math Consortium, 2008) Department of Mathematics; Etgü, Tolga; Faculty Member; Department of Mathematics; College of Sciences; 16206
    This is a brief summary of recent examples of isotopically different symplectic and Lagrangian surfaces representing a fixed homology class in a simply-connected symplectic 4-manifold.
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    Elliptic open books on torus bundles over the circle
    (Springer, 2008) Department of Mathematics; Etgü, Tolga; Faculty Member; Department of Mathematics; College of Sciences; 16206
    As an application of the construction of open books on plumbed 3-manifolds, we construct elliptic open books on torus bundles over the circle. In certain cases these open books are compatible with Stein fillable contact structures and have minimal genus.
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    Examples of planar tight contact structures with support norm one
    (Oxford Univ Press, 2010) Lekili, Yankı; Department of Mathematics; Etgü, Tolga; Faculty Member; Department of Mathematics; College of Sciences; 16206
    We exhibit an infinite family of tight contact structures with the property that none of the supporting open books minimizes the genus and maximizes the Euler characteristic of the page simultaneously. This answers a question of Baldwin and Etnyre in [2].
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    Symplectic tori in rational elliptic surfaces
    (Springer, 2006) Park, B. Doug; Department of Mathematics; Etgü, Tolga; Faculty Member; Department of Mathematics; College of Sciences; 16206
    Let E(1)(p) denote the rational elliptic surface with a single multiple fiber f(p) of multiplicity p. We construct an infinite family of homologous non-isotopic symplectic tori representing the primitive 2-dimensional homology class [f(p)] in E(1)(p) when p > 1. As a consequence, we get infinitely many non-isotopic symplectic tori in the fiber class of the rational elliptic surface E(1) = CP2# 9 (CP) over bar (2). We also show how these tori can be non-isotopically embedded as homologous symplectic submanifolds in other symplectic 4-manifolds.
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    Nonfillable legendrian knots in the 3-sphere
    (Geometry and Topology Publications, 2018) Department of Mathematics; Etgü, Tolga; Faculty Member; Department of Mathematics; College of Sciences
    If Lambda is a Legendrian knot in the standard contact 3-sphere that bounds an orientable exact Lagrangian surface Sigma in the standard symplectic 4-ball, then the genus of Sigma is equal to the slice genus of (the smooth knot underlying) Lambda, the rotation number of a is zero as well as the sum of the Thurston-Bennequin number of Lambda and the Euler characteristic of Sigma, and moreover, the linearized contact homology of Lambda with respect to the augmentation induced by Sigma is isomorphic to the (singular) homology of Sigma. It was asked by Ekholm, Honda and Kalman (2016) whether the converse of this statement holds. We give a negative answer, providing a family of Legendrian knots with augmentations which are not induced by any exact Lagrangian filling although the associated linearized contact homology is isomorphic to the homology of the smooth surface of minimal genus in the 4-ball bounding the knot.
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    A note on fundamental groups of symplectic torus complements in 4-manifolds
    (World Scientific Publ Co Pte Ltd, 2008) Park, B. Doug; Department of Mathematics; Etgü, Tolga; Faculty Member; Department of Mathematics; College of Sciences; 16206
    Previously, we constructed an infinite family of knotted symplectic tori representing a fixed homology class in the symplectic four-manifold E(n) K, which is obtained by Fintushel-Stern knot surgery using a nontrivial fibered knot K in S-3, and distinguished the (smooth) isotopy classes of these tori by indirectly computing the Seiberg-Witten invariants of their complements. In this note, we compute the fundamental groups of the complements of these knotted tori and show that for each nontrivial fibered knot K these groups constitute an infinite collection of nonisomorphic groups. We also review some other constructions of symplectic tori in 4-manifolds and show that the fundamental groups of the complements do not distinguish homologous tori in those cases.
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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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    Homologous non-isotopic symplectic tori in homotopy rational elliptic surfaces
    (Cambridge University Press (CUP), 2006) Park, B. Doug; Department of Mathematics; Etgü, Tolga; Faculty Member; Department of Mathematics; College of Sciences; 16206
    Let E(1)(K) denote the homotopy rational elliptic surface corresponding to a knot K in S-3 constructed by R. Fintushel and R. J. Stern. We construct an infinite family of homologous non-isotopic symplectic tori representing a primitive 2-dimensional homology class in E(1)(K) when K is any nontrivial fibred knot in S-3. We also show how these tori can be non-isotopically embedded as homologous symplectic submanifolds in other symplectic 4-manifolds.
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    On the contact Ozsváth–Szabó invariant
    (Akademiai Kiado Zrt, 2010) 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
    Sarkar and Wang proved that the hat version of Heegaard Floer homology group of a closed oriented 3-manifold is combinatorial starting from an arbitrary nice Heegaard diagram and in fact every closed oriented 3-manifold admits such a Heegaard diagram. Plamenevskaya showed that the contact Ozsvath-Szabo invariant is combinatorial once we are given an open book decomposition compatible with a contact structure. The idea is to combine the algorithm of Sarkar and Wang with the recent description of the contact Ozsvath-Szabo invariant due to Honda, Kazez and Matic. Here we observe that the hat version of the Heegaard Floer homology group and the contact Ozsvath-Szabo invariant in this group can be combinatorially calculated starting from a contact surgery diagram. We give detailed examples pointing out to some shortcuts in the computations.
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    Lagrangian tori in homotopy elliptic surfaces
    (American Mathematical Society (AMS), 2005) Mckinnon, David; Park, B. Doug; Department of Mathematics; Etgü, Tolga; Faculty Member; Department of Mathematics; College of Sciences; 16206
    Let E( 1)(K) denote the symplectic four-manifold, homotopy equivalent to the rational elliptic surface, corresponding to a. bred knot K in S-3 constructed by R. Fintushel and R. J. Stern in 1998. We construct a family of nullhomologous Lagrangian tori in E( 1)(K) and prove that infinitely many of these tori have complements with mutually non-isomorphic fundamental groups if the Alexander polynomial of K has some irreducible factor which does not divide t(n) - 1 for any positive integer n. We also show how these tori can be non-isotopically embedded as nullhomologous Lagrangian submanifolds in other symplectic 4-manifolds.