Lectures on symplectic geometry

• Published in: Lecture notes in mathematics Vol. 1764
• Main Author: Silva, Ana Cannas da
• Format: eBook Book
• Language: English
• Published: Berlin, Heidelberg Springer-Verlag 2008; Springer Berlin / Heidelberg; Springer Berlin Heidelberg; Springer
• Edition: 1
• Series: Lecture 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
• ISBN: 9783540421955; 3540421955
• ISSN: 0075-8434; 1617-9692
• DOI: 10.1007/978-3-540-45330-7

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, Kaehler manifolds, hamiltonian mechanics, moments 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.