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To set the stage for our development, we begin this book with a treatment of the basic features of symplectic geometry. By a symplectic manifold we mean an even-dimensional differentiable (C ∞) manifold M 2n n together with a global 2-form Ω which is closed and of maximal rank, i.e., dΩ = 0, Ω n ≠ 0. By a symplectomorphism f: (M 1, Ω1) → (M 2, Ω2) we mean a diffeomorphism f : M 1 → M 2 such that f*Ω2 =Ω1.
KeywordsSymplectic Form Symplectic Manifold Betti Number Cotangent Bundle Lagrangian Submanifold
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