This volume presents some of the lectures and research during the special programme held at the Newton Institute in 1994. The book, in two parts, begins with an introductory overview. The two parts each contain a mix of substantial expository articles and research papers that outline important and topical ideas. Many of the results have not been presented before. Symplectic methods are one of the most active areas of research in mathematics currently, and this volume will attract much attention.
• Symplectic geometry is a hot topic • This is the first time much of this material has been available in print form • Top contributors in subject
Contents
Preface; Contributors; Introduction; Part I. Geometric Methods: 1. J-curves and the classification of rational and ruled symplectic 4-manifolds François Lalonde and Dusa McDuff; 2. Periodic Hamiltonian flows on four dimensional manifolds Yael Karshon; 3. 3-Dimensional contact geometry (based on lectures of Y. Eliashberg and E. Giroux) C. B. Thomas; 4. Topology and analysis of contact circles Hansjörg Geiges and Jesús Gonzalo; 5. Properties of pseudoholomorphic curves in symplectisation IV: asymptotics with degeneracies H. Hofer, K. Wysocki and E. Zehnder; 6. Pseudo-holomorphic curves and Bernoulli shifts Kai Cieliebak; 7. On closed trajectories of a charge in a magnetic field. An application of symplectic geometry Viktor L. Ginzburg; Part II. Symplectic Invariants: 8. Introduction to symplectic Floer homology Matthias Schwarz; 9. Symplectic Floer-Donaldson theory and quantum cohomology S. Piunikhin, D. Salamon and M. Schwarz; 10. Relative Floer and quantum cohomology and the symplectic topology of Lagrangian submanifolds Yong-Geun Oh; 11. Cup-length estimate for symplectic fixed points Lê Hông Vân and Kaoru Ono; 12. Hofer's symplectic energy and Lagrangian intersections Yu V. Chekanov; 13. On the existence of symplectic submanifolds (from lectures of S. Donaldson) C. B. Thomas.
Review
‘… this volume will attract much attention.’ L’Enseignement Mathématique
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