Ana CannasdaSilva September 2004

• fiche de synthèse - matière potentielle : hodge theory for kahler manifolds

Symplectic Geometry overview written for the Handbook of Differential Geometry, vol. 2 (F.J.E. Dillen and L.C.A. Verstraelen, eds.) Ana Cannas da Silva∗ September 2004 Contents Introduction 3 1 Symplectic Manifolds 5 1.1 Symplectic Linear Algebra . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Symplectic Forms . . . . . . . . .

• terms of exterior algebra
• flow of a vector field
• map ω
• symplectic manifolds
• symplectic forms
• lagrangian subspace
• cotangent bundles
• differential geometry
• symplectic geometry