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 was… Expand

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

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) is… Expand

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 Seidel… Expand

"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 of… Expand

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 calculates… Expand