Weak symplectic fillings and holomorphic curves

Klaus Niederkrüger; Chris Wendl

Displaying similar documents to “Weak symplectic fillings and holomorphic curves”

A generalization of the normal holomorphic frames in symplectic manifolds

Luigi Vezzoni (2006)

Bollettino dell'Unione Matematica Italiana

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In this paper we give a generalization of the normal holomorphic frames in symplectic manifolds and find conditions for the integrability of complex structures.

Gluing complex discs to Lagrangian manifolds by Gromov’s method

Alexandre Sukhov, Alexander Tumanov (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

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The paper discusses some aspects of Gromov’s theory of gluing complex discs to Lagrangian manifolds.

Fano manifolds of degree ten and EPW sextics

Atanas Iliev, Laurent Manivel (2011)

Annales scientifiques de l'École Normale Supérieure

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O’Grady showed that certain special sextics in $ℙ^{5}$ called EPW sextics admit smooth double covers with a holomorphic symplectic structure. We propose another perspective on these symplectic manifolds, by showing that they can be constructed from the Hilbert schemes of conics on Fano fourfolds of degree ten. As applications, we construct families of Lagrangian surfaces in these symplectic fourfolds, and related integrable systems whose fibers are intermediate Jacobians.

Examples of compact holomorphic symplectic mainfolds which are not Kählerian II.

Daniel Guan (1995)

Inventiones mathematicae

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Pseudo holomorphic curves in symplectic manifolds.

M. Gromov (1985)

Inventiones mathematicae

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A vanishing theorem for twisted Alexander polynomials with applications to symplectic 4-manifolds

Stefan Friedl, Stefano Vidussi (2013)

Journal of the European Mathematical Society

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In this paper we show that given any 3-manifold $N$ and any non-fibered class in $H^{1} (N; Z)$ there exists a representation such that the corresponding twisted Alexander polynomial is zero. We obtain this result by extending earlier work of ours and by combining this with recent results of Agol and Wise on separability of 3-manifold groups. This result allows us to completely classify symplectic 4-manifolds with a free circle action, and to determine their symplectic cones.

Fundamental group of $Symp (M, ω)$ with no circle action

Jarek Kędra (2009)

Archivum Mathematicum

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We show that $π_{1} (Symp (M, ω))$ can be nontrivial for $M$ that does not admit any symplectic circle action.

The Seiberg-Witten invariants of symplectic four-manifolds

Dieter Kotschick (1995-1996)

Séminaire Bourbaki

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On symplectic fillings.

Etnyre, John B. (2004)

Algebraic & Geometric Topology

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On the number of components of the symplectic representatives of the canonical class

Stefano Vidussi (2007)

Journal of the European Mathematical Society

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We show that there exists a family of simply connected, symplectic 4-manifolds such that the (Poincaré dual of the) canonical class admits both connected and disconnected symplectic representatives. This answers a question raised by Fintushel and Stern.

On Seiberg-Witten equationsοn symplectic 4-manifolds

Klaus Mohnke (1997)

Banach Center Publications

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We discuss Taubes' idea to perturb the monopole equations on symplectic manifolds to compute the Seiberg-Witten invariants in the light of Witten's symmetry trick in the Kähler case.