Contact and Symplectic Geometry

'… this volume will attract much attention.' L'Enseignement Mathématique

• 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.