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Lectures on Symplectic Geometry

  • Ana Cannas da Silva

Part of the Lecture Notes in Mathematics book series (LNM, volume 1764)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Symplectic Manifolds

    1. Front Matter
      Pages 2-2
    2. Ana Cannas da Silva
      Pages 3-8
    3. Ana Cannas da Silva
      Pages 9-14
  3. Symplectomorphisms

    1. Front Matter
      Pages 16-16
    2. Ana Cannas da Silva
      Pages 17-23
    3. Ana Cannas da Silva
      Pages 25-31
    4. Ana Cannas da Silva
      Pages 33-37
  4. Local Forms

    1. Front Matter
      Pages 40-40
    2. Ana Cannas da Silva
      Pages 41-47
    3. Ana Cannas da Silva
      Pages 49-53
    4. Ana Cannas da Silva
      Pages 55-60
    5. Ana Cannas da Silva
      Pages 61-66
  5. Contact Manifolds

    1. Front Matter
      Pages 68-68
    2. Ana Cannas da Silva
      Pages 69-74
    3. Ana Cannas da Silva
      Pages 75-79
  6. Compatible Almost Complex Structures

    1. Front Matter
      Pages 82-82
    2. Ana Cannas da Silva
      Pages 83-88
    3. Ana Cannas da Silva
      Pages 89-92
    4. Ana Cannas da Silva
      Pages 93-98
  7. Kähler Manifolds

    1. Front Matter
      Pages 100-100
    2. Ana Cannas da Silva
      Pages 101-107
    3. Ana Cannas da Silva
      Pages 109-116
    4. Ana Cannas da Silva
      Pages 117-123
  8. Hamiltonian Mechanics

    1. Front Matter
      Pages 126-126
    2. Ana Cannas da Silva
      Pages 127-134
    3. Ana Cannas da Silva
      Pages 135-142
    4. Ana Cannas da Silva
      Pages 143-148
  9. Moment Maps

    1. Front Matter
      Pages 150-150
    2. Ana Cannas da Silva
      Pages 151-156
    3. Ana Cannas da Silva
      Pages 157-163
  10. Symplectic Reduction

    1. Front Matter
      Pages 166-166
    2. Ana Cannas da Silva
      Pages 167-171
    3. Ana Cannas da Silva
      Pages 173-179
  11. Moment Maps Revisited

    1. Front Matter
      Pages 182-182
    2. Ana Cannas da Silva
      Pages 183-192
    3. Ana Cannas da Silva
      Pages 193-198
    4. Ana Cannas da Silva
      Pages 199-205
  12. Symplectic Toric Manifolds

    1. Front Matter
      Pages 208-208
    2. Ana Cannas da Silva
      Pages 209-214
    3. Ana Cannas da Silva
      Pages 215-222
    4. Ana Cannas da Silva
      Pages 223-231
  13. Back Matter
    Pages 233-247

About this book

Introduction

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, 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.

There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster.

For this reprint numerous corrections and clarifications have been made, and the layout has been improved.

Keywords

differential geometry geometry hamiltonian manifold symplectic symplectic geometry

Authors and affiliations

  • Ana Cannas da Silva
    • 1
  1. 1.Department of MathematicsPrinceton University08544-1000PrincetonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-45330-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-42195-5
  • Online ISBN 978-3-540-45330-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site