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Symplectic Topology and Floer Homology: Volume 1, Symplectic Geometry and Pseudoholomorphic Curves: New Mathematical Monographs, cartea 28

Autor Yong-Geun Oh
en Limba Engleză Hardback – 26 aug 2015
Published in two volumes, this is the first book to provide a thorough and systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole. Volume 1 covers the basic materials of Hamiltonian dynamics and symplectic geometry and the analytic foundations of Gromov's pseudoholomorphic curve theory. One novel aspect of this treatment is the uniform treatment of both closed and open cases and a complete proof of the boundary regularity theorem of weak solutions of pseudo-holomorphic curves with totally real boundary conditions. Volume 2 provides a comprehensive introduction to both Hamiltonian Floer theory and Lagrangian Floer theory. Symplectic Topology and Floer Homology is a comprehensive resource suitable for experts and newcomers alike.
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Specificații

ISBN-13: 9781107072459
ISBN-10: 110707245X
Pagini: 420
Ilustrații: 35 b/w illus. 50 exercises
Dimensiuni: 159 x 236 x 31 mm
Greutate: 0.79 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria New Mathematical Monographs

Locul publicării:New York, United States

Cuprins

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, ω); 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.

Notă biografică


Descriere

The first part of a two-volume set offering a systematic explanation of symplectic topology. This volume covers the basic materials of Hamiltonian dynamics and symplectic geometry.