Lectures On Symplectic Geometry

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Lectures on Symplectic Geometry

Ana Cannas da Silva
Lectures on Symplectic Geometry Book PDF

Author : Ana Cannas da Silva
Publisher : Springer
Page : 220 pages
File Size : 54,6 Mb
Release : 2004-10-27
Category : Mathematics
ISBN : 9783540453307

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Lectures on Symplectic Geometry by Ana Cannas da Silva Pdf

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.

Lectures on Symplectic Manifolds

Alan Weinstein
Lectures on Symplectic Manifolds Book PDF

Author : Alan Weinstein
Publisher : American Mathematical Soc.
Page : 48 pages
File Size : 54,7 Mb
Release : 1977
Category : Mathematics
ISBN : 9780821816790

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Lectures on Symplectic Manifolds by Alan Weinstein Pdf

The first six sections of these notes contain a description of some of the basic constructions and results on symplectic manifolds and lagrangian submanifolds. Section 7, on intersections of largrangian submanifolds, is still mostly internal to symplectic geometry, but it contains some applications to machanics and dynamical systems. Sections 8, 9, and 10 are devoted to various aspects of the quantization problem. In Section 10 there is a feedback of ideas from quantization theory into symplectic geometry itslef.

Lectures on Poisson Geometry

Marius Crainic,Rui Loja Fernandes,Ioan Mărcuţ
Lectures on Poisson Geometry Book PDF

Author : Marius Crainic,Rui Loja Fernandes,Ioan Mărcuţ
Publisher : American Mathematical Soc.
Page : 479 pages
File Size : 55,9 Mb
Release : 2021-10-14
Category : Education
ISBN : 9781470466671

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Lectures on Poisson Geometry by Marius Crainic,Rui Loja Fernandes,Ioan Mărcuţ Pdf

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

Lectures on the Geometry of Quantization

Sean Bates,Alan Weinstein
Lectures on the Geometry of Quantization Book PDF

Author : Sean Bates,Alan Weinstein
Publisher : American Mathematical Soc.
Page : 150 pages
File Size : 50,8 Mb
Release : 1997
Category : Mathematics
ISBN : 0821807986

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Lectures on the Geometry of Quantization by Sean Bates,Alan Weinstein Pdf

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.

Contact and Symplectic Geometry

Charles Benedict Thomas
Contact and Symplectic Geometry Book PDF

Author : Charles Benedict Thomas
Publisher : Cambridge University Press
Page : 332 pages
File Size : 49,8 Mb
Release : 1996-09-28
Category : Mathematics
ISBN : 0521570867

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Contact and Symplectic Geometry by Charles Benedict Thomas Pdf

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.

Symplectic Geometry and Topology

Yakov Eliashberg,Lisa M. Traynor
Symplectic Geometry and Topology Book PDF

Author : Yakov Eliashberg,Lisa M. Traynor
Publisher : American Mathematical Soc.
Page : 452 pages
File Size : 55,5 Mb
Release : 2004
Category : Mathematics
ISBN : 0821886894

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Symplectic Geometry and Topology by Yakov Eliashberg,Lisa M. Traynor Pdf

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.

Introduction to Symplectic Topology

Dusa McDuff,Dietmar Salamon
Introduction to Symplectic Topology Book PDF

Author : Dusa McDuff,Dietmar Salamon
Publisher : Oxford University Press
Page : 637 pages
File Size : 42,5 Mb
Release : 2017
Category : Mathematics
ISBN : 9780198794899

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Introduction to Symplectic Topology by Dusa McDuff,Dietmar Salamon Pdf

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.

Lectures on the Geometry of Poisson Manifolds

Izu Vaisman
Lectures on the Geometry of Poisson Manifolds Book PDF

Author : Izu Vaisman
Publisher : Birkhäuser
Page : 210 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034884952

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Lectures on the Geometry of Poisson Manifolds by Izu Vaisman Pdf

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.

Symplectic 4-Manifolds and Algebraic Surfaces

Denis Auroux,Fabrizio Catanese,Marco Manetti,Gang Tian,Paul Seidel,Ivan Smith,Bernd Siebert
Symplectic 4 Manifolds and Algebraic Surfaces Book PDF

Author : Denis Auroux,Fabrizio Catanese,Marco Manetti,Gang Tian,Paul Seidel,Ivan Smith,Bernd Siebert
Publisher : Springer Science & Business Media
Page : 363 pages
File Size : 47,5 Mb
Release : 2008-04-17
Category : Mathematics
ISBN : 9783540782780

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Symplectic 4-Manifolds and Algebraic Surfaces by Denis Auroux,Fabrizio Catanese,Marco Manetti,Gang Tian,Paul Seidel,Ivan Smith,Bernd Siebert Pdf

Modern approaches to the study of symplectic 4-manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration. Gauge theory, symplectic geometry, pseudoholomorphic curves, singularity theory, moduli spaces, braid groups, monodromy, in addition to classical topology and algebraic geometry, combine to make this one of the most vibrant and active areas of research in mathematics. It is our hope that the five lectures of the present volume given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003 will be useful to people working in related areas of mathematics and will become standard references on these topics. The volume is a coherent exposition of an active field of current research focusing on the introduction of new methods for the study of moduli spaces of complex structures on algebraic surfaces, and for the investigation of symplectic topology in dimension 4 and higher.

J-holomorphic Curves and Symplectic Topology

Dusa McDuff,Dietmar Salamon
J holomorphic Curves and Symplectic Topology Book PDF

Author : Dusa McDuff,Dietmar Salamon
Publisher : American Mathematical Soc.
Page : 744 pages
File Size : 40,6 Mb
Release : 2012
Category : Pseudoholomorphic curves
ISBN : 9780821887462

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J-holomorphic Curves and Symplectic Topology by Dusa McDuff,Dietmar Salamon Pdf

The main goal of this book is to establish the fundamental theorems of the subject in full and rigourous detail. In particular, the book contains complete proofs of Gromov's compactness theorem for spheres, of the gluing theorem for spheres, and of the associatively of quantum multiplication in the semipositive case. The book can also serve as an introduction to current work in symplectic topology.

Symplectic Geometry

Dietmar Salamon
Symplectic Geometry Book PDF

Author : Dietmar Salamon
Publisher : Cambridge University Press
Page : 246 pages
File Size : 55,7 Mb
Release : 1993
Category : Mathematics
ISBN : 9780521446990

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Symplectic Geometry by Dietmar Salamon Pdf

This volume is based on lectures given at a workshop and conference on symplectic geometry at the University of Warwick in August 1990.

Lectures in Geometric Combinatorics

Rekha R. Thomas
Lectures in Geometric Combinatorics Book PDF

Author : Rekha R. Thomas
Publisher : American Mathematical Soc.
Page : 156 pages
File Size : 41,8 Mb
Release : 2006
Category : Mathematics
ISBN : 0821841408

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Lectures in Geometric Combinatorics by Rekha R. Thomas Pdf

This book presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. The book starts with the basics of polytope theory. Schlegel and Gale diagrams are introduced as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes. The heart of the book is a treatment of the secondary polytope of a point configuration and its connections to the statepolytope of the toric ideal defined by the configuration. These polytopes are relatively recent constructs with numerous connections to discrete geometry, classical algebraic geometry, symplectic geometry, and combinatorics. The connections rely on Grobner bases of toric ideals and other methods fromcommutative algebra. The book is self-contained and does not require any background beyond basic linear algebra. With numerous figures and exercises, it can be used as a textbook for courses on geometric, combinatorial, and computational aspects of the theory of polytopes.

Symplectic Geometry and Topology

Yakov Eliashberg
Symplectic Geometry and Topology Book PDF

Author : Yakov Eliashberg
Publisher : Unknown
Page : 430 pages
File Size : 53,6 Mb
Release : 1999
Category : Symplectic manifolds
ISBN : 1470439069

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Symplectic Geometry and Topology by Yakov Eliashberg Pdf

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: Introduction to Symplectic Topology by D. McDuff; Holomorphic Curves and Dynamics in Dimension Three by H. Hofer; An Introduct.

Symplectic Geometry of Integrable Hamiltonian Systems

Michèle Audin,Ana Cannas da Silva,Eugene Lerman
Symplectic Geometry of Integrable Hamiltonian Systems Book PDF

Author : Michèle Audin,Ana Cannas da Silva,Eugene Lerman
Publisher : Birkhäuser
Page : 225 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880718

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Symplectic Geometry of Integrable Hamiltonian Systems by Michèle Audin,Ana Cannas da Silva,Eugene Lerman Pdf

Among all the Hamiltonian systems, the integrable ones have special geometric properties; in particular, their solutions are very regular and quasi-periodic. This book serves as an introduction to symplectic and contact geometry for graduate students, exploring the underlying geometry of integrable Hamiltonian systems. Includes exercises designed to complement the expositiont, and up-to-date references.

Introduction to Symplectic Geometry

Jean-Louis Koszul,Yi Ming Zou
Introduction to Symplectic Geometry Book PDF

Author : Jean-Louis Koszul,Yi Ming Zou
Publisher : Springer
Page : 121 pages
File Size : 55,5 Mb
Release : 2019-04-15
Category : Science
ISBN : 9789811339875

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Introduction to Symplectic Geometry by Jean-Louis Koszul,Yi Ming Zou Pdf

This introductory book offers a unique and unified overview of symplectic geometry, highlighting the differential properties of symplectic manifolds. It consists of six chapters: Some Algebra Basics, Symplectic Manifolds, Cotangent Bundles, Symplectic G-spaces, Poisson Manifolds, and A Graded Case, concluding with a discussion of the differential properties of graded symplectic manifolds of dimensions (0,n). It is a useful reference resource for students and researchers interested in geometry, group theory, analysis and differential equations.This book is also inspiring in the emerging field of Geometric Science of Information, in particular the chapter on Symplectic G-spaces, where Jean-Louis Koszul develops Jean-Marie Souriau's tools related to the non-equivariant case of co-adjoint action on Souriau’s moment map through Souriau’s Cocycle, opening the door to Lie Group Machine Learning with Souriau-Fisher metric.