Introductions to Symplectic Geometry   Andrew Dancer

1. (1) symplectic forms  (2) symplectic manifolds
2. Local theory of Symplectic manifolds (1) Isotopy  (2) Moser theorem  (3) Darboux theorem
3. Coadjoint Orbit
4. (Lie)group Action on Symplectic manifolds
5. Reduced Space
6. Convexity theorem
7. Toric Actions on Symplectic manifolds
8. Gromov School
9. Hamiltonian Mechanics

例子 [Kahler manifold]  [cotangent bundle]

歷史

1. Darboux定理   Alan Weinstein定理
2. M.Gromov  ---Pseudo-holomorphic curve     Gromov-Witten invariant
   Theory of J-holomorphic curves which led to the creation of Symplectic topology and became linked to quantum field theory
   convex integratin Almost flat manifolds 3-d Heisenberg group
   Grpmov : Every manifold admitting a sequence of metrics such that the diameter and curvature go to zero is finitely covered by a nilmanifold
   Collapse with bounded curvature
3. (1) V.I.Arnold   (2) Andreas Floer
4. 鏡像對稱 (1) Maxim Kontsevch  (2) 深谷賢治(Kenji Fukaya)

科學的Sym化      Mikhael Gromov (1943~  )

1. Introductions to Symplectic Geometry   Andrew Dancer
2. Symplectic geometry and Topology       V.I.Arnold
3. An Introduction to Lie Groups and Symplectic Geometry   Robert L. Bryant
4. Lectures on Symplectic Geometry           Ana Cannas da Silva
5. First steps in Symplectic Topology         V.I.Arnold
6. Differential Geometry with Applications to Mechanics and Physics (Lecture 10) Yves Talpaert