Overview
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.
Full Product Details
Author: Ana Cannas da Silva
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition: 1st Corrected ed. 2001. Corr. 2nd printing 2008
Volume: 1764
Dimensions:
Width: 15.50cm
, Height: 1.40cm
, Length: 23.50cm
Weight: 0.840kg
ISBN: 9783540421955
ISBN 10: 3540421955
Pages: 220
Publication Date: 17 July 2001
Audience:
College/higher education
,
Professional and scholarly
,
Undergraduate
,
Postgraduate, Research & Scholarly
Format: Paperback
Publisher's Status: Active
Availability: In Print
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.
Reviews
From the reviews of the first printing <p>Over the years, there have been several books written to serve as an introduction to symplectic geometry and topology, [a ]] The text under review here fits well within this tradition, providing a useful and effective synopsis of the basics of symplectic geometry and possibly serving as the springboard for a prospective researcher. <p>The material covered here amounts to the usual suspects of symplectic geometry and topology. From an introductory chapter of symplectic forms and symplectic algebra, the book moves on to many of the subjects that serve as the basis for current research: symplectomorphisms, Lagrangian submanifolds, the Moser theorems, Darboux-Moser-Weinstein theory, almost complex structures, KAhler structures, Hamiltonian mechanics, symplectic reduction, etc. <p>The text is written in a clear, easy-to-follow style, that is most appropriate in mathematical sophistication for second-year graduate students; [a ]]. <p>This text had its origins in a 15-week course that the author taught at UC Berkeley. There are some nice passages where the author simply lists some known results and some well-known conjectures, much as one would expect to see in a good lecture on the same subject. Particularly eloquent is the authora (TM)s discussion of the compact examples and counterexamples of symplectic, almost complex, complex and KAhler manifolds. <p>Throughout the text, she uses specific, well-chosen examples to illustrate the results. In the initial chapter, she provides a detailed section on the classical example of the syrnplectic structure of the cotangent bundle of a manifold. <p>Showing a good sense of pedagogy, the authoroften leaves these examples as well-planned homework assignments at the end of some of the sections. [a ]] In all of these cases, the author gives the reader a chance to illustrate and understand the interesting results of each section, rather than relegating the tedious but needed results to the reader. <p>Mathematical Reviews 2002i
From the reviews of the first printing Over the years, there have been several books written to serve as an introduction to symplectic geometry and topology, [!] The text under review here fits well within this tradition, providing a useful and effective synopsis of the basics of symplectic geometry and possibly serving as the springboard for a prospective researcher. The material covered here amounts to the usual suspects of symplectic geometry and topology. From an introductory chapter of symplectic forms and symplectic algebra, the book moves on to many of the subjects that serve as the basis for current research:symplectomorphisms, Lagrangian submanifolds, the Moser theorems, Darboux-Moser-Weinstein theory, almost complex structures, Kahler structures, Hamiltonian mechanics, symplectic reduction, etc. The text is written in a clear, easy-to-follow style, that is most appropriate in mathematical sophistication for second-year graduate students; [!]. This text had its origins in a 15-week course that the author taught at UC Berkeley. There are some nice passages where the author simply lists some known results and some well-known conjectures, much as one would expect to see in a good lecture on the same subject. Particularly eloquent is the author's discussion of the compact examples and counterexamples of symplectic, almost complex, complex and Kahler manifolds. Throughout the text, she uses specific, well-chosen examples to illustrate the results. In the initial chapter, she provides a detailed section on the classical example of the syrnplectic structure of the cotangent bundle of a manifold. Showing a good sense of pedagogy, the author often leaves these examples as well-planned homework assignments at the end of some of the sections. [!] In all of these cases, the author gives the reader a chance to illustrate and understand the interesting results of each section, rather than relegating the tedious but needed results to the reader. Mathematical Reviews 2002i
