Lectures on symplectic geometry

>> Google Books

所蔵情報QRコード

Lectures on symplectic geometry / Ana Cannas da Silva

資料種別:: 図書
出版情報:: Berlin ; New York : Springer-Verlag, c2001
形態:: xii, 217 p. ; 24 cm
シリーズ名:: Lecture notes in mathematics ; 1764 <BA00146586>
著者名:: Silva, Ana Cannas da <DA13228566>
ISBN:: 9783540421955 [3540421955]
書誌ID:: BA53082947

子書誌情報

フルテキスト

所蔵情報

他の版・巻

Lectures on symplectic geometry. Corr. 2. print
Ana Cannas da Silva , Springer-Verlag , 2008

書誌詳細

注記:

Bibliography: p. [199]-206
Includes index

主題:

Geometry, Differential; Symplectic manifolds

言語:

英語

目次情報:

Foreword

Introduction

Symplectic Manifolds / I：

Symplectic Forms / 1：

Skew-Symmetric Bilinear Maps / 1.1：

Symplectic Vector Spaces / 1.2：

Symplectomorphisms / 1.3：

Symplectic Linear Algebra / Homework 1：

Symplectic Form on the Cotangent Bundle / 2：

Cotangent Bundle / 2.1：

Tautological and Canonical Forms in Coordinates / 2.2：

Coordinate-Free Definitions / 2.3：

Naturality of the Tautological and Canonical Forms / 2.4：

Symplectic Volume / Homework 2：

Lagrangian Submanifolds / II：

Submanifolds / 3.1：

Lagrangian Submanifolds of T*X / 3.2：

Conormal Bundles / 3.3：

Application to Symplectomorphisms / 3.4：

Tautological Form and Symplectomorphisms / Homework 3：

Generating Functions / 4：

Constructing Symplectomorphisms / 4.1：

Method of Generating Functions / 4.2：

Application to Geodesic Flow / 4.3：

Geodesic Flow / Homework 4：

Recurrence / 5：

Periodic Points / 5.1：

Billiards / 5.2：

PoincarÃ© Recurrence / 5.3：

Local Forms / III：

Preparation for the Local Theory / 6：

Isotopies and Vector Fields / 6.1：

Tubular Neighborhood Theorem / 6.2：

Homotopy Formula / 6.3：

Moser Theorems / Homework 5：

Notions of Equivalence for Symplectic Structures / 7.1：

Moser Trick / 7.2：

Moser Local Theorem / 7.3：

Darboux-Moser-Weinstein Theory / 8：

Classical Darboux Theorem / 8.1：

Lagrangian Subspaces / 8.2：

Weinstein Lagrangian Neighborhood Theorem / 8.3：

Oriented Surfaces / Homework 6：

Weinstein Tubular Neighborhood Theorem / 9：

Observation from Linear Algebra / 9.1：

Tubular Neighborhoods / 9.2：

Application 1: Tangent Space to the Group of Symplectomorphisms / 9.3：

Application 2: Fixed Points of Symplectomorphisms / 9.4：

Contact Manifolds / IV：

Contact Forms / 10：

Contact Structures / 10.1：

Examples / 10.2：

First Properties / 10.3：

Manifolds of Contact Elements / Homework 7：

Contact Dynamics / 11：

Reeb Vector Fields / 11.1：

Symplectization / 11.2：

Conjectures of Seifert and Weinstein / 11.3：

Compatible Almost Complex Structures / V：

Almost Complex Structures / 12：

Three Geometries / 12.1：

Complex Structures on Vector Spaces / 12.2：

Compatible Structures / 12.3：

Compatible Linear Structures / Homework 8：

Compatible Triples / 13：

Compatibility / 13.1：

Triple of Structures / 13.2：

First Consequences / 13.3：

Contractibility / Homework 9：

Dolbeault Theory / 14：

Splittings / 14.1：

Forms of Type (l, m) / 14.2：

J-Holomorphic Functions / 14.3：

Dolbeault Cohomology / 14.4：

Integrability / Homework 10：

KÃ¤hler Manifolds / VI：

Complex Manifolds / 15：

Complex Charts / 15.1：

Forms on Complex Manifolds / 15.2：

Differentials / 15.3：

Complex Projective Space / Homework 11：

KÃ¤hler Forms / 16：

An Application / 16.1：

Recipe to Obtain KÃ¤hler Forms / 16.3：

Local Canonical Form for KÃ¤hler Forms / 16.4：

The Fubini-Study Structure / Homework 12：

Compact KÃ¤hler Manifolds / 17：

Hodge Theory / 17.1：

Immediate Topological Consequences / 17.2：

Compact Examples and Counterexamples / 17.3：

Main KÃ¤hler Manifolds / 17.4：

Hamiltonian Mechanics / VII：

Hamiltonian Vector Fields / 18：

Hamiltonian and Symplectic Vector Fields / 18.1：

Classical Mechanics / 18.2：

Brackets / 18.3：

Integrable Systems / 18.4：

Simple Pendulum / Homework 13：

Variational Principles / 19：

Equations of Motion / 19.1：

Principle of Least Action / 19.2：

Variational Problems / 19.3：

Solving the Euler-Lagrange Equations / 19.4：

Minimizing Properties / 19.5：

Minimizing Geodesies / Homework 14：

Legendre Transform / 20：

Strict Convexity / 20.1：

Application to Variational Problems / 20.2：

Moment Maps / Homework 15：

Actions / 21：

One-Parameter Groups of Diffeomorphisms / 21.1：

Lie Groups / 21.2：

Smooth Actions / 21.3：

Symplectic and Hamiltonian Actions / 21.4：

Adjoint and Coadjoint Representations / 21.5：

Hermitian Matrices / Homework 16：

Hamiltonian Actions / 22：

Moment and Comoment Maps / 22.1：

Orbit Spaces / 22.2：

Preview of Reduction / 22.3：

Classical Examples / 22.4：

Coadjoint Orbits / Homework 17：

Symplectic Reduction / IX：

The Marsden-Weinstein-Meyer Theorem / 23：

Statement / 23.1：

Ingredients / 23.2：

Proof of the Marsden-Weinstein-Meyer Theorem / 23.3：

Reduction / 24：

Noether Principle / 24.1：

Elementary Theory of Reduction / 24.2：

Reduction for Product Groups / 24.3：

Reduction at Other Levels / 24.4：

Orbifolds / 24.5：

Spherical Pendulum / Homework 18：

Moment Maps Revisited / X：

Moment Map in Gauge Theory / 25：

Connections on a Principal Bundle / 25.1：

Connection and Curvature Forms / 25.2：

Symplectic Structure on the Space of Connections / 25.3：

Action of the Gauge Group / 25.4：

Case of Circle Bundles / 25.5：

Examples of Moment Maps / Homework 19：

Existence and Uniqueness of Moment Maps / 26：

Lie Algebras of Vector Fields / 26.1：

Lie Algebra Cohomology / 26.2：

Existence of Moment Maps / 26.3：

Uniqueness of Moment Maps / 26.4：

Examples of Reduction / Homework 20：

Convexity / 27：

Convexity Theorem / 27.1：

Effective Actions / 27.2：

Connectedness / 27.3：

Symplectic Toric Manifolds / XI：

Classification of Symplectic Toric Manifolds / 28：

Delzant Polytopes / 28.1：

Delzant Theorem / 28.2：

Sketch of Delzant Construction / 28.3：

Delzant Construction / 29：

Algebraic Set-Up / 29.1：

The Zero-Level / 29.2：

Conclusion of the Delzant Construction / 29.3：

Idea Behind the Delzant Construction / 29.4：

Duistermaat-Heckman Theorems / Homework 22：

Duistermaat-Heckman Polynomial / 30.1：

Local Form for Reduced Spaces / 30.2：

Variation of the Symplectic Volume / 30.3：

References / Homework 23：

Index

Foreword

Introduction

Symplectic Manifolds / I：

Symplectic Forms / 1：

Skew-Symmetric Bilinear Maps / 1.1：

Symplectic Vector Spaces / 1.2：

続きを見る

東工大ブックレビュー

類似資料:

1 図書 Lectures on symplectic geometry Silva, Ana Cannas da Springer-Verlag	7 図書 Symplectic geometry and topology (: pbk) Eliashberg, Y., 1946-, Traynor, Lisa (Lisa M.), 1964- American Mathematical Society, Institute for Advanced Study
2 電子ブック Lectures on Symplectic Geometry Silva, Ana Cannas da, Takens, F. SpringerLink Books - AutoHoldings, Springer Berlin Heidelberg	8 図書 Gauge theory and symplectic geometry NATO Advanced Study Institute and Séminaire de mathématiques supérieures on Gauge Theory and Symplectic Geometry, … Kluwer Academic Publishers
3 図書 Contact and symplectic geometry Thomas, Charles Benedict Cambridge University Press	9 図書 Holomorphic curves in symplectic geometry (: us ; : sz) Audin, Michèle, Lafontaine, J. (Jacques), 1944 Mar. 10-, CIMPA summer school Birkhäuser
4 図書 Symplectic geometry and its applications (: us ; : gw) Arnolʹd, Vladimir Igorevich, 1937-, Novikov, Sergeĭ Petrovich Springer-Verlag	10 図書 Symplectic geometry Fomenko, Anatoliĭ Timofeevich, Wadhwa, R. S. Gordon and Breach
5 図書 Symplectic and contact topology : interactions and perspectives Eliashberg, Y., 1946-, Khesin, Boris E. (Boris Emmanuel), 1932-, Lalonde, François American Mathematical Society	11 図書 Symplectic geometry Fomenko, Anatoliĭ Timofeevich, Wadhwa, R. S. Gordon and Breach
6 図書 Representation theory and complex geometry Chriss, Neil, 1967-, Ginzburg, Victor, 1957- Birkhäuser	12 図書 Symplectic geometry and secondary characteristic classes (: us ; : gw) Vaisman, Izu Birkhäuser