CONTENTS
Introduction ............................................................................................................................................ .
Lecture 1. Symplectic manifolds and lagrangian submanifolds, examples ................................... 3
Lecture 2. Lagrangian splittings, real and complex polarizations, Kahler manifolds............... 7
Lecture 3. Reduction, the calculus of canonical relations, intermediate polarizations ........... .11
Lecture 4. Hamiltonian systems and group actions on symplectic manifolds ........................... 15
Lecture 5. Normal forms ..................................................................................................................... 22
Lecture 6. Lagrangian submanifolds and families of functions ................................................... 25
Lecture 7. Intersection Theory of lagrangian submanifolds ......................................................... 29
Lecture 8. Quantization on cotangent bundles ............................................................................... 31
Lecture 9. Quantization and polarizations ....................................................................................... 35
Lecture IO. Quantizing lagrangian submanifolds and subspaces, construction of the Maslov
bundle .................................................................................................................................................. 39
References ................................................................................................................................................ 45
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