Item description for Lectures on Symplectic Geometry (Lecture Notes in Mathematics) by Ana Cannas Da Silva & Ana Cannas Da Silva...
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.
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Reviews - What do customers think about Lectures on Symplectic Geometry (Lecture Notes in Mathematics)?
Difficult as to be expected... May 27, 2008
On the one hand, it's a good and fairly complete book on modern symplectic geometry and Hamiltonian systems, but on the other hand it is extremely dense without any illuminating examples, which makes reading it very difficult. Unfortunately, the concise lecture notes style is typical in mathematics today, so there aren't many alternatives if you want a book that deals with most of the theory.
In order to read and understand the book you probably have to be an advanced graduate student in mathematics with a clear affinity towards minimalistic, sentence-free lemma-proof-theorem-proof texts. As a textbook I cannot recommend these Lectures on Symplectic Geometry, as they are too dense, too proof-oriented and too example-devoid. As a quick reference for young researchers in mathematics who already master the rudiments of symplectic topology and geometry it might be an inexpensive possibility. For all others (the actually intended audience, i.e. the interested students who want to learn about symplectic geometry) it is a non-risk-free investment: you have to take the time and go very slowly through the material and either you are rewarded for your great efforts eventually or you are stuck at trivialities and become discouraged unduly.