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Symplectic geometry and pseudoholomorphic curves

Yong‐Geun Oh

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Abstract

Preface Part I. Hamiltonian Dynamics and Symplectic Geometry: 1. Least action principle and the Hamiltonian mechanics 2. Symplectic manifolds and Hamilton's equation 3. Lagrangian submanifolds 4. Symplectic fibrations 5. Hofer's geometry of Ham(M, omega) 6. C0-Symplectic topology and Hamiltonian dynamics Part II. Rudiments of Pseudoholomorphic Curves: 7. Geometric calculations 8. Local study of J-holomorphic curves 9. Gromov compactification and stable maps 10. Fredholm theory 11. Applications to symplectic topology References Index.

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Preface Part I. Hamiltonian Dynamics and Symplectic Geometry: 1. Least action principle and the Hamiltonian mechanics 2. Symplectic manifolds and Hamilton's equation 3. Lagrangian submanifolds 4. Symplectic fibrations 5. Hofer's geometry of Ham(M, omega) 6. C0-Symplectic topology and Hamiltonian dynamics Part II. Rudiments of Pseudoholomorphic Curves: 7. Geometric calculations 8. Local study of J-holomorphic curves 9. Gromov compactification and stable maps 10. Fredholm theory 11. Applications to symplectic topology References Index.

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Available abstract

Preface Part I. Hamiltonian Dynamics and Symplectic Geometry: 1. Least action principle and the Hamiltonian mechanics 2. Symplectic manifolds and Hamilton's equation 3. Lagrangian submanifolds 4. Symplectic fibrations 5. Hofer's geometry of Ham(M, omega) 6. C0-Symplectic topology and Hamiltonian dynamics Part II. Rudiments of Pseudoholomorphic Curves: 7. Geometric calculations 8. Local study of J-holomorphic curves 9. Gromov compactification and stable maps 10. Fredholm theory 11. Applications to symplectic topology References Index.

Key concepts: Symplectic geometry, Symplectomorphism, Mathematics, Symplectic manifold, Moment map, Geometry and topology, Hamiltonian mechanics, Floer homology

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