Normal view MARC view ISBD view

Silva, Ana Cannas da

Lectures on symplectic geometry - German: Springer, [c2001] - 247 p.

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 Kähler Manifolds
15. Complex Manifolds
16. Kähler Forms
17. Compact Kähler Manifolds

VII Hamiltonian Mechanics
18. Hamiltonian Vector Fields
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. Delzant Construction
30. Duistermaat-Heckman Theorems


This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding.

ISBN: 9783540421955

LC Class. No.: QA3 / 01213