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Look Inside Symplectic Topology and Floer Homology

Symplectic Topology and Floer Homology

Volume 1. Symplectic Geometry and Pseudoholomorphic Curves

Part of New Mathematical Monographs

Author: Yong-Geun Oh, IBS Center for Geometry and Physics, and Pohang University of Science and Technology, Republic of Korea

Date Published: September 2015
availability: Available
format: Hardback
isbn: 9781107072459

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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.
- Covers both open and closed pseudoholomorphic curves in general genus for those who want to learn basic analytic techniques in symplectic topology
- Explanations of basic symplectic geometry and Hamiltonian dynamics up to continuous category reveal the connection between pre-Gromov and post-Gromov symplectic geometry
- Includes self-contained explanations of basic Floer homology both open and closed and of its applications for those who want to teach themselves the basic Floer homology
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Product details
- Date Published: September 2015
- format: Hardback
- isbn: 9781107072459
- length: 420 pages
- dimensions: 236 x 159 x 31 mm
- weight: 0.77kg
- contains: 35 b/w illus. 50 exercises
- availability: Available
Table of Contents
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.
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Author
Yong-Geun Oh, IBS Center for Geometry and Physics, and Pohang University of Science and Technology, Republic of Korea
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.