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 covers symplectomorphisms, local forms, contact manifold, compatible almost complex structures, Kaeh...

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Bibliographic Details
Published inLecture notes in mathematics Vol. 1764
Main Author Silva, Ana Cannas da
Format eBook Book
LanguageEnglish
Published Berlin, Heidelberg Springer-Verlag 2008
Springer Berlin / Heidelberg
Springer Berlin Heidelberg
Springer
Edition1
SeriesLecture Notes in Mathematics
Subjects
Differential Geometry
Exact sciences and technology
General mathematics
General, history and biography
Geometry, Differential
Mathematics
Mathematics and Statistics
Partial Differential Equations
Sciences and techniques of general use
Symplectic geometry
Symplectic manifolds
Mathematics
Online AccessGet full text
ISBN9783540421955
3540421955
ISSN0075-8434
1617-9692
DOI10.1007/978-3-540-45330-7

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Table of Contents:
  • Intro -- Foreword -- Contents -- Introduction -- Part I Symplectic Manifolds -- Chapter 1 Symplectic Forms -- Chapter 2 Symplectic Form on the Cotangent Bundle -- Part II Symplectomorphisms -- Chapter 3 Lagrangian Submanifolds -- Chapter 4 Generating Functions -- Chapter 5 Recurrence -- Part III Local Forms -- Chapter 6 Preparation for the Local Theory -- Chapter 7 Moser Theorems -- Chapter 8 Darboux-Moser-Weinstein Theory -- Chapter 9 Weinstein Tubular Neighborhood Theorem -- Part IV Contact Manifolds -- Chapter 10 Contact Forms -- Chapter 11 Contact Dynamics -- Part V Compatible Almost Complex Structures -- Chapter 12 Almost Complex Structures -- Chapter 13 Compatible Triples -- Chapter 14 Dolbeault Theory -- Part VI Kahler Manifolds -- Chapter 15 Complex Manifolds -- Chapter 16 Kahler Forms -- Chapter 17 Compact Kahler Manifolds -- Part VII Hamiltonian Mechanics -- Chapter 18 Hamiltonian Vector Fields -- Chapter 19 Variational Principles -- Chapter 20 Legendre Transform -- Part VIII Moment Maps -- Chapter 21 Actions -- Chapter 22 Hamiltonian Actions -- Part IX Symplectic Reduction -- Chapter 23 The Marsden-Weinstein-Meyer Theorem -- Chapter 24 Reduction -- Part X Moment Maps Revisited -- Chapter 25 Moment Map in Gauge Theory -- Chapter 26 Existence and Uniqueness of Moment Maps -- Chapter 27 Convexity -- Part XI Symplectic Toric Manifolds -- Chapter 28 Classification of Symplectic Toric Manifolds -- Chapter 29 Delzant Construction -- Chapter 30 Duistermaat-Heckman Theorems -- References -- Index