| Description |
1 online resource (637 pages) |
| Series |
Oxford Graduate Texts in Mathematics |
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Oxford graduate texts in mathematics ; 27.
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| Contents |
Cover; Preface ; Preface to the second edition; Preface to the third edition; Contents; Introduction; I Foundations; 1 From classical to modern; 1.1 Hamiltonian mechanics; 1.2 The symplectic topology of Euclidean space; 2 Linear symplectic geometry; 2.1 Symplectic vector spaces; 2.2 The symplectic linear group; 2.3 Lagrangian subspaces; 2.4 The affine nonsqueezing theorem; 2.5 Linear complex structures; 2.6 Symplectic vector bundles; 2.7 First Chern class; 3 Symplectic manifolds; 3.1 Basic concepts; 3.2 Moser isotopy and Darboux's theorem; 3.3 Isotopy extension theorems |
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3.4 Submanifolds of symplectic manifolds3.5 Contact structures; 4 Almost complex structures; 4.1 Almost complex structures; 4.2 Integrability; 4.3 Kähler manifolds; 4.4 Kähler surfaces; 4.5 J-holomorphic curves; II Symplectic manifolds; 5 Symplectic group actions; 5.1 Circle actions; 5.2 Moment maps; 5.3 Examples; 5.4 Symplectic quotients; 5.5 Convexity; 5.6 Localization; 5.7 Remarks on GIT; 6 Symplectic Fibrations; 6.1 Symplectic fibrations; 6.2 Symplectic 2-sphere bundles; 6.3 Symplectic connections; 6.4 Hamiltonian holonomy and the coupling form; 6.5 Hamiltonian fibrations |
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7 Constructing Symplectic Manifolds7.1 Blowing up and down; 7.2 Connected sums; 7.3 The telescope construction; 7.4 Donaldson submanifolds; III Symplectomorphisms; 8 Area-preserving diffeomorphisms; 8.1 Periodic orbits; 8.2 The Poincaré-Birkhoff theorem; 8.3 The billiard problem; 9 Generating functions; 9.1 Generating functions and symplectic action; 9.2 Discrete Hamiltonian mechanics; 9.3 Hamiltonian symplectomorphisms; 9.4 Lagrangian submanifolds; 10 The group of symplectomorphisms; 10.1 Basic properties; 10.2 The flux homomorphism; 10.3 The Calabi homomorphism |
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10.4 The topology of symplectomorphism groupsIV Symplectic invariants; 11 The Arnold conjecture; 11.1 Symplectic fixed points; 11.2 Morse theory and the Conley index; 11.3 Lagrangian intersections; 11.4 Floer homology; 12 Symplectic capacities; 12.1 Nonsqueezing and capacities; 12.2 Rigidity; 12.3 The Hofer metric; 12.4 The Hofer-Zehnder capacity; 12.5 A variational argument; 13 Questions of existence and uniqueness; 13.1 Existence and uniqueness of symplectic structures; 13.2 Examples; 13.3 Taubes-Seiberg-Witten theory; 13.4 Symplectic four-manifolds; 14 Open problems |
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14.1 Symplectic structures14.2 Symplectomorphisms; 14.3 Lagrangian submanifolds and cotangent bundles; 14.4 Fano manifolds; 14.5 Donaldson hypersurfaces; 14.6 Contact geometry; 14.7 Continuous symplectic topology; 14.8 Symplectic embeddings; 14.9 Symplectic topology of Euclidean space; Appendix A Smooth maps; A.1 Smooth functions on manifolds with corners; A.2 Extension; A.3 Construction of a smooth function; References; Index |
| Summary |
Over the last number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. This new third edition of a classic book in the feild includes updates and new material to bring the material right up-to-date |
| Bibliography |
Includes bibliographical references (pages 583-610) and index |
| Notes |
Print version record |
| Subject |
Symplectic manifolds.
|
|
Topology.
|
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MATHEMATICS -- Topology.
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Symplectic manifolds
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Topology
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| Form |
Electronic book
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| Author |
Salamon, D. (Dietmar), author.
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| ISBN |
0192514016 |
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9780192514011 |
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9780191836411 |
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0191836419 |
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