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Lectures on Symplectic Geometry by Ana Cannas da Silva

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About this book :-
Lectures on Symplectic Geometry written by Ana Cannas da Silva

Book Detail :-
Title: Lectures on Symplectic Geometry
Edition:
Author(s): Ana Cannas da Silva
Publisher:
Series: Lecture Notes in Mathematics 629
Year: 2006
Pages: 225
Type: PDF
Language: English
ISBN:
Country:
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Book Contents :-
Lectures on Symplectic Geometry written by Ana Cannas da Silva cover the following topics.
I Symplectic Manifolds
1. Symplectic Forms
2. Symplectic Form on the Cotangent Bundle
II Symplectomorphisms
3. Lagrangian Submanifolds
4. Generating Functions
5. Recurrence
III Local Forms
6. Preparation for the Local Theory
7. Moser Theorems
8. Darboux-Moser-Weinstein Theory
9. Weinstein Tubular Neighborhood Theorem
IV Contact Manifolds
10. Contact Forms
11. Contact Dynamics V Compatible Almost Complex Structures
12. Almost Complex Structures
13. Compatible Triples
14. Dolbeault Theory
VI K¨ahler Manifolds
15. Complex Manifolds
16. K¨ahler Forms
17. Compact K¨ahler Manifolds
VII Hamiltonian Mechanics
18. Hamiltonian Vector Fields
19. Variational Principles
20. Legendre Transform
VII Hamiltonian Mechanics
19 Variational Principles
20 Legendre Transform
VIII Moment Maps
21. Actions
22. Hamiltonian Actions
IX Symplectic Reduction
23. The Marsden-Weinstein-Meyer Theorem
24. Reduction
X Moment Maps Revisited
25. Moment Map in Gauge Theory
26. Existence and Uniqueness of Moment Maps
27. Convexity
XI Symplectic Toric Manifolds
28. Classification of Symplectic Toric Manifolds
29.0Delzant Construction
30. Duistermaat-Heckman Theorems


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