Lectures on Symplectic Geometry

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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Detalles Bibliográficos
Autor principal: Cannas da Silva, Ana. author (author)
Formato: Libro electrónico
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg 2008.
Edición:1st ed. 2008.
Colección:Lecture Notes in Mathematics, 1764
Materias:
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009461780906719
Tabla de Contenidos:
  • 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.