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Lectures on Symplectic Geometry

By Silva, Ana Cannas Da

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Book Id: WPLBN0003761781
Format Type: PDF eBook :
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Reproduction Date: 2015

Title: Lectures on Symplectic Geometry  
Author: Silva, Ana Cannas Da
Volume:
Language: English
Subject: Programming, Mathematics, Geometry
Collections: Technical Books Center
Historic
Publication Date:
2006
Publisher: Springer-verlag

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Da Silva, A. C. (2006). Lectures on Symplectic Geometry. Retrieved from http://kindle.worldlibrary.net/


Description
Description: This note contains on the following subtopics of Symplectic Geometry, Symplectic Manifolds, Symplectomorphisms, Local Forms, Contact Manifolds, Compatible Almost Complex Structures, Kahler Manifolds, Hamiltonian Mechanics, Moment Maps, Symplectic Reduction, Moment Maps Revisited and Symplectic Toric Manifolds.

Table of Contents
TOC : Introduction - I Symplectic Manifolds - 1 Symplectic Forms - Homework 1: Symplectic Linear Algebra - 2 Symplectic Form on the Cotangent Bundle - Homework 2: Symplectic Volume - II Symplectomorphisms - 3 Lagrangian Submanifolds - Homework 3: Tautological Form and Symplectomorphisms - 4 Generating Functions - Homework 4: Geodesic Flow - 5 Recurrence - III Local Forms - 6 Preparation for the Local Theory - Homework 5: Tubular Neighborhoods in Rn - 7 Moser Theorems - 8 Darboux-Moser-Weinstein Theory - Homework 6: Oriented Surfaces - 9 Weinstein Tubular Neighborhood Theorem - IV Contact Manifolds - 10 Contact Forms - Homework 7: Manifolds of Contact Elements - 11 Contact Dynamics - V Compatible Almost Complex Structures - 12 Almost Complex Structures - Homework 8: Compatible Linear Structures - 13 Compatible Triples - Homework 9: Contractibility - 14 Dolbeault Theory - Homework 10: Integrability - VI K¨ahler Manifolds - 15 Complex Manifolds - Homework 11: Complex Projective Space - 16 K¨ahler Forms - Homework 12: The Fubini-Study Structure - 17 Compact K¨ahler Manifolds - VII Hamiltonian Mechanics - 18 Hamiltonian Vector Fields - Homework 13: Simple Pendulum - 19 Variational Principles - Homework 14: Minimizing Geodesics - 20 Legendre Transform - Homework 15: Legendre Transform - VIII Moment Maps - 21 Actions - Homework 16: Hermitian Matrices - 22 Hamiltonian Actions - Homework 17: Coadjoint Orbits - IX Symplectic Reduction - 23 The Marsden-Weinstein-Meyer Theorem - 24 Reduction - Homework 18: Spherical Pendulum - X Moment Maps Revisited - 25 Moment Map in Gauge Theory - Homework 19: Examples of Moment Maps - 26 Existence and Uniqueness of Moment Maps - Homework 20: Examples of Reduction - 27 Convexity - Homework 21: Connectedness - XI Symplectic Toric Manifolds - 28 Classification of Symplectic Toric Manifolds - 29 Delzant Construction - Homework 22: Delzant Theorem - 30 Duistermaat-Heckman Theorems - Homework 23: S1-Equivariant Cohomology - References - Index.

 

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