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J-Holomorphic Curves and Symplectic Topology
The theory of $J$-holomorphic curves has been of great importance since its introduction by Gromov in 1985. In mathematics, its applications include many key results in symplectic topology. It wasExpand
Introduction to Symplectic Topology
Introduction I. FOUNDATIONS 1. From classical to modern 2. Linear symplectic geometry 3. Symplectic manifolds 4. Almost complex structures II. SYMPLECTIC MANIFOLDS 5. Symplectic group actions 6.Expand
The structure of rational and ruled symplectic 4-manifolds
This paper investigates the structure of compact symplectic 4-manifolds (V, w) which contain a symplectically embedded copy C of S2 with nonnegative self-intersection number. Such a pair (V, C, w) isExpand
J-Holomorphic Curves and Quantum Cohomology
Introduction Local behaviour Moduli spaces and transversality Compactness Compactification of moduli spaces Evaluation maps and transversality Gromov-Witten invariants Quantum cohomology NovikovExpand
Topological properties of Hamiltonian circle actions
This paper studies Hamiltonian circle actions, i.e. circle subgroups of the group Ham(M,ω) of Hamiltonian symplectomorphisms of a closed symplectic manifold (M,ω). Our main tool is the SeidelExpand
The geometry of symplectic energy
"Non-Squeezing Theorem" which says that it is impossible to embed a large ball symplectically into a thin cylinder of the form R2, x B2, where B2 is a 2-disc. This led to Hofer's discovery ofExpand
Topology of symplectomorphism groups of rational ruled surfaces
Let M be either S 2 S 2 or the one point blow-up CP 2 # CP 2 of CP 2 . In both cases M carries a family of symplectic forms ! , where > 1 determines the cohomology class [! ]. This paper calculatesExpand