Yong-Geun Oh

Symplectic Topology and Floer Homology: Volume 1, Symplectic Geometry and Pseudoholomorphic Curves (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 27. August 2015
• Englisch
• ISBN-13: 9781316379349
• Artikelnr.: 53005427

Autorenporträt

Yong-Geun Oh is Director of the IBS Center for Geometry and Physics and is Professor in the Department of Mathematics at POSTECH (Pohang University of Science and Technology) in Korea. He was also Professor in the Department of Mathematics at the University of Wisconsin, Madison. He is a member of the KMS, the AMS, the Korean National Academy of Sciences, and the inaugural class of AMS Fellows. In 2012 he received the Kyung-Ahm Prize for Science in Korea.

Inhaltsangabe

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, ¿)
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.