Fredholm theory of holomorphic discs under the perturbation of boundary conditions

DOI10.1007/PL00004544zbMath0863.53024MaRDI QIDQ2365057

Yong-Geun Oh

Publication date: 12 June 1997

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174898

zbMATH Keywords

Kähler manifoldLagrangian submanifoldMaslov indexpseudo-holomorphic discsHamiltonian diffeomorphismsFredholm-regularperturbation by Lagrangian isotopies

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) (Semi-) Fredholm operators; index theories (47A53) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Global submanifolds (53C40) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Analytic subsets and submanifolds (32C25) Complex manifolds (32Q99)

Related Items (14)

Exact Lagrangian immersions with a single double point ⋮ Quasistabilization and basepoint moving maps in link Floer homology ⋮ Regularity of discs attached to a submanifold of \(\mathbb{C}^n\) ⋮ A wrapped Fukaya category of knot complement ⋮ An introduction to knot Floer homology ⋮ Harmonic discs of solutions to the complex homogeneous Monge-Ampère equation ⋮ Filtering the Heegaard Floer contact invariant ⋮ Relative frames on \(J\)-holomorphic curves ⋮ Fredholm-regularity of holomorphic discs in plane bundles over compact surfaces ⋮ Defect and evaluations ⋮ A cylindrical reformulation of Heegaard Floer homology ⋮ On the structure of pseudo-holomorphic discs with totally real boundary conditions ⋮ Framed bordism and Lagrangian embeddings of exotic spheres ⋮ Geometry of Kähler metrics and foliations by holomorphic discs

Cites Work

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• Symplectic fixed points, the Calabi invariant and Novikov homology. [Appendix C in collaboration with Lê Tu Quôc Thang]
• Symplectic displacement energy for Lagrangian submanifolds
• The unregularized gradient flow of the symplectic action
• Floer cohomology of lagrangian intersections and pseudo‐holomorphic disks I
• The Maslov Class of the Lagrange Surfaces and Gromov's Pseudo-Holomorphic Curves

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