Lectures on symplectic geometry

By: Silva, Ana Cannas daMaterial type: TextTextPublication details: German: Springer, [c2001]Description: 247 pISBN: 9783540421955Subject(s): MathematicsLOC classification: QA3
Contents:
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
Summary: 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.
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Mathematic Rack No 3 QA3 (Browse shelf (Opens below)) Available Billno:IN 00562; Billdate: 2018-05-03 01146
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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.

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