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Lectures on symplectic geometry / Ana Cannas da Silva.

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The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures,...

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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Silva, Ana Cannas da
Format: eBook
Language:English
Published: Berlin ; New York : Springer, ©2001.
Series:Lecture notes in mathematics (Springer-Verlag) ; 1764.
Subjects:
Symplectic geometry.
Table of Contents:
  • Symplectic Manifolds
  • Symplectic Forms
  • Symplectic Form on the Cotangent Bundle
  • Symplectomorphisms
  • Lagrangian Submanifolds
  • Generating Functions
  • Recurrence
  • Local Forms
  • Preparation for the Local Theory
  • Moser Theorems
  • Darboux-Moser-Weinstein Theory
  • Weinstein Tubular Neighborhood Theorem
  • Contact Manifolds
  • Contact Forms
  • Contact Dynamics
  • Compatible Almost Complex Structures
  • Almost Complex Structures
  • Compatible Triples
  • Dolbeault Theory
  • Kähler Manifolds
  • Complex Manifolds
  • Kähler Forms
  • Compact Kähler Manifolds
  • Hamiltonian Mechanics
  • Hamiltonian Vector Fields
  • Variational Principles
  • Legendre Transform
  • Moment Maps
  • Actions
  • Hamiltonian Actions
  • Symplectic Reduction
  • The Marsden-Weinstein-Meyer Theorem
  • Reduction
  • Moment Maps Revisited
  • Moment Map in Gauge Theory
  • Existence and Uniqueness of Moment Maps
  • Convexity
  • Symplectic Toric Manifolds
  • Classification of Symplectic Toric Manifolds
  • Delzant Construction
  • Duistermaat-Heckman Theorems.

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