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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.
Table of contents:
Introduction; Part I. Geometric Methods: 1. J-holomorphic spheres and the classification of rational and ruled symplectic 4-manifolds F. Lalonde and D. McDuff; 2. Periodic Hamiltonian flows on 4-dimensional manifolds Y. Karshon; 3. 3-dimensional contact geometry C. B. Thomas (based on lectures by Y. Eliashberg and E. Giroux); 4. Topology and analysis of contact circles H. Geiges and J. Gonzalo; 5. Pseudoholomorphic curves and Bernoulli shifts K. Cieliebak; 6. On closed trajectories of a charge moving in a magnetic field - an application of symplectic geometry V. Ginzburg; 7. Properties of pseudoholomorphic curves in symplectisations IV: Asymptotics with degeneracies H. Hofer, K. Wysocki and E. Zehnder; Part II. Symplectic Invariants: 8. Introduction to symplectic Floer homology and cohomology operations from S1-cobordisms M. Schwarz; 8. 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 Y. G. Oh; 11. Cup-length estimates for symplectic fixed points K. Ono and L. H. Van; 12. Hofer's symplectic energy and Lagrangian intersections Y. Chekanov; 13. On the existence of symplectic submanifolds C. B. Thomas (based on lectures by S. K. Donaldson).
This volume presents some of the lectures and research during the special programme held at the Newton Institute in 1994. It contains a mix of substantial expository articles and research papers that outline important and topical ideas. Many of the results have not been presented before.
Another volume on symplectic methods; these sell well!
Table of contents:
Introduction; Part I. Geometric Methods: 1. J-holomorphic spheres and the classification of rational and ruled symplectic 4-manifolds F. Lalonde and D. McDuff; 2. Periodic Hamiltonian flows on 4-dimensional manifolds Y. Karshon; 3. 3-dimensional contact geometry C. B. Thomas (based on lectures by Y. Eliashberg and E. Giroux); 4. Topology and analysis of contact circles H. Geiges and J. Gonzalo; 5. Pseudoholomorphic curves and Bernoulli shifts K. Cieliebak; 6. On closed trajectories of a charge moving in a magnetic field - an application of symplectic geometry V. Ginzburg; 7. Properties of pseudoholomorphic curves in symplectisations IV: Asymptotics with degeneracies H. Hofer, K. Wysocki and E. Zehnder; Part II. Symplectic Invariants: 8. Introduction to symplectic Floer homology and cohomology operations from S1-cobordisms M. Schwarz; 8. 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 Y. G. Oh; 11. Cup-length estimates for symplectic fixed points K. Ono and L. H. Van; 12. Hofer's symplectic energy and Lagrangian intersections Y. Chekanov; 13. On the existence of symplectic submanifolds C. B. Thomas (based on lectures by S. K. Donaldson).
This volume presents some of the lectures and research during the special programme held at the Newton Institute in 1994. It contains a mix of substantial expository articles and research papers that outline important and topical ideas. Many of the results have not been presented before.
Another volume on symplectic methods; these sell well!