Lectures On Symplectic Geometry
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Author |
: Ana Cannas da Silva |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 240 |
Release |
: 2001-07-17 |
ISBN-10 |
: 9783540421955 |
ISBN-13 |
: 3540421955 |
Rating |
: 4/5 (55 Downloads) |
Synopsis Lectures on Symplectic Geometry by : 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.
Author |
: Ana Cannas da Silva |
Publisher |
: Springer |
Total Pages |
: 240 |
Release |
: 2004-10-27 |
ISBN-10 |
: 9783540453307 |
ISBN-13 |
: 354045330X |
Rating |
: 4/5 (07 Downloads) |
Synopsis Lectures on Symplectic Geometry by : 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.
Author |
: Yakov Eliashberg |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 452 |
Release |
: 2004 |
ISBN-10 |
: 0821886894 |
ISBN-13 |
: 9780821886892 |
Rating |
: 4/5 (94 Downloads) |
Synopsis Symplectic Geometry and Topology by : Yakov Eliashberg
Symplectic geometry has its origins as a geometric language for classical mechanics. But it has recently exploded into an independent field interconnected with many other areas of mathematics and physics. The goal of the IAS/Park City Mathematics Institute Graduate Summer School on Symplectic Geometry and Topology was to give an intensive introduction to these exciting areas of current research. Included in this proceedings are lecture notes from the following courses: Introductionto Symplectic Topology by D. McDuff; Holomorphic Curves and Dynamics in Dimension Three by H. Hofer; An Introduction to the Seiberg-Witten Equations on Symplectic Manifolds by C. Taubes; Lectures on Floer Homology by D. Salamon; A Tutorial on Quantum Cohomology by A. Givental; Euler Characteristicsand Lagrangian Intersections by R. MacPherson; Hamiltonian Group Actions and Symplectic Reduction by L. Jeffrey; and Mechanics: Symmetry and Dynamics by J. Marsden. Information for our distributors: Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Author |
: Marius Crainic |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 479 |
Release |
: 2021-10-14 |
ISBN-10 |
: 9781470466671 |
ISBN-13 |
: 1470466678 |
Rating |
: 4/5 (71 Downloads) |
Synopsis Lectures on Poisson Geometry by : Marius Crainic
This excellent book will be very useful for students and researchers wishing to learn the basics of Poisson geometry, as well as for those who know something about the subject but wish to update and deepen their knowledge. The authors' philosophy that Poisson geometry is an amalgam of foliation theory, symplectic geometry, and Lie theory enables them to organize the book in a very coherent way. —Alan Weinstein, University of California at Berkeley This well-written book is an excellent starting point for students and researchers who want to learn about the basics of Poisson geometry. The topics covered are fundamental to the theory and avoid any drift into specialized questions; they are illustrated through a large collection of instructive and interesting exercises. The book is ideal as a graduate textbook on the subject, but also for self-study. —Eckhard Meinrenken, University of Toronto
Author |
: Dusa McDuff |
Publisher |
: Oxford University Press |
Total Pages |
: 637 |
Release |
: 2017 |
ISBN-10 |
: 9780198794899 |
ISBN-13 |
: 0198794894 |
Rating |
: 4/5 (99 Downloads) |
Synopsis Introduction to Symplectic Topology by : Dusa McDuff
Over the last number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. This new third edition of a classic book in the feild includes updates and new material to bring the material right up-to-date.
Author |
: Alan Weinstein |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 58 |
Release |
: 1977 |
ISBN-10 |
: 9780821816790 |
ISBN-13 |
: 0821816799 |
Rating |
: 4/5 (90 Downloads) |
Synopsis Lectures on Symplectic Manifolds by : Alan Weinstein
Features notes with sections containing a description of some of the basic constructions and results on symplectic manifolds and lagrangian submanifolds. This title also includes sections dealing with various aspects of the quantization problem, as wel as those giving a feedback of ideas from quantization theory into symplectic geometry itslef.
Author |
: Sean Bates |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 150 |
Release |
: 1997 |
ISBN-10 |
: 0821807986 |
ISBN-13 |
: 9780821807989 |
Rating |
: 4/5 (86 Downloads) |
Synopsis Lectures on the Geometry of Quantization by : Sean Bates
These notes are based on a course entitled ``Symplectic Geometry and Geometric Quantization'' taught by Alan Weinstein at the University of California, Berkeley (fall 1992) and at the Centre Emile Borel (spring 1994). The only prerequisite for the course needed is a knowledge of the basic notions from the theory of differentiable manifolds (differential forms, vector fields, transversality, etc.). The aim is to give students an introduction to the ideas of microlocal analysis and the related symplectic geometry, with an emphasis on the role these ideas play in formalizing the transition between the mathematics of classical dynamics (hamiltonian flows on symplectic manifolds) and quantum mechanics (unitary flows on Hilbert spaces). These notes are meant to function as a guide to the literature. The authors refer to other sources for many details that are omitted and can be bypassed on a first reading.
Author |
: Izu Vaisman |
Publisher |
: Birkhäuser |
Total Pages |
: 210 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783034884952 |
ISBN-13 |
: 3034884958 |
Rating |
: 4/5 (52 Downloads) |
Synopsis Lectures on the Geometry of Poisson Manifolds by : Izu Vaisman
This book is addressed to graduate students and researchers in the fields of mathematics and physics who are interested in mathematical and theoretical physics, differential geometry, mechanics, quantization theories and quantum physics, quantum groups etc., and who are familiar with differentiable and symplectic manifolds. The aim of the book is to provide the reader with a monograph that enables him to study systematically basic and advanced material on the recently developed theory of Poisson manifolds, and that also offers ready access to bibliographical references for the continuation of his study. Until now, most of this material was dispersed in research papers published in many journals and languages. The main subjects treated are the Schouten-Nijenhuis bracket; the generalized Frobenius theorem; the basics of Poisson manifolds; Poisson calculus and cohomology; quantization; Poisson morphisms and reduction; realizations of Poisson manifolds by symplectic manifolds and by symplectic groupoids and Poisson-Lie groups. The book unifies terminology and notation. It also reports on some original developments stemming from the author's work, including new results on Poisson cohomology and geometric quantization, cofoliations and biinvariant Poisson structures on Lie groups.
Author |
: Charles Benedict Thomas |
Publisher |
: Cambridge University Press |
Total Pages |
: 332 |
Release |
: 1996-09-28 |
ISBN-10 |
: 0521570867 |
ISBN-13 |
: 9780521570862 |
Rating |
: 4/5 (67 Downloads) |
Synopsis Contact and Symplectic Geometry by : Charles Benedict Thomas
This volume presents some of the lectures and research during the special programme held at the Newton Institute in 1994. The two parts each contain a mix of substantial expository articles and research papers that outline important and topical ideas. Many of the results have not been presented before, and the lectures on Floer homology is the first avaliable in book form.Symplectic methods are one of the most active areas of research in mathematics currently, and this volume will attract much attention.
Author |
: Dietmar Salamon |
Publisher |
: Cambridge University Press |
Total Pages |
: 246 |
Release |
: 1993 |
ISBN-10 |
: 9780521446990 |
ISBN-13 |
: 0521446996 |
Rating |
: 4/5 (90 Downloads) |
Synopsis Symplectic Geometry by : Dietmar Salamon
This volume is based on lectures given at a workshop and conference on symplectic geometry at the University of Warwick in August 1990.