Lectures on Symplectic Geometry, Numéro 1764Springer Science & Business Media, 17 juil. 2001 - 217 pages 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. |
Table des matières
Symplectic Linear Algebra | 8 |
Symplectic Volume | 14 |
Recurrence | 33 |
Tubular Neighborhoods in | 47 |
8 | 55 |
Contact Manifolds | 67 |
Contact Dynamics | 75 |
Almost Complex Structures | 83 |
Minimizing Geodesics | 141 |
Legendre Transform | 147 |
Hermitian Matrices | 156 |
Coadjoint Orbits | 163 |
Reduction | 173 |
Moment Maps Revisited | 182 |
Examples of Moment Maps | 191 |
Examples of Reduction | 198 |
Compatible Triples | 89 |
Integrability | 98 |
Complex Projective Space | 107 |
The FubiniStudy Structure | 115 |
Compact Kähler Manifolds | 117 |
Hamiltonian Mechanics | 126 |
Simple Pendulum | 134 |
Connectedness | 204 |
Symplectic Toric Manifolds | 208 |
Delzant Construction | 215 |
Delzant Theorem | 221 |
References | 233 |