Symplectic Topology and Floer Homology
Symplectic Topology and Floer Homology
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
Product details
No date availableAdobe eBook Reader
9781316382943
0 pages
0kg
35 b/w illus. 50 exercises
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.
