1549055384-Symplectic_Geometry_and_Topology__Eliashberg_

Contents

Preface

Introduction

Dusa McDuff, Introduction to Symplectic Topology

Introduction

Lecture 1. Basics

Existence of Many Symplectomorphisms

Linear Symplectic Geometry

The Cotangent Bundle

Lecture 2. Moser's Argument

Lecture 3. The Linear Theory

w-Compatible Almost Complex Structures

Vector Bundles

The Lagrangian Grassmannian

The Maslov Index

Lecture 4. The Nonsqueezing Theorem and Capacities

Preliminaries on J-Holomorphic Curves

Lecture 5. Sketch Proof of the Nonsqueezing Theorem

Fredholm Theory

Compactness

Bibliography

Helmut Hofer, Holomorphic Curves and Dynamics in Dimension

Three

Lecture 1. Problems, Basic Concepts and Overview
Periodic Orbits of Smooth Vector Fields on Three-Manifolds
Holomorphic Curves and Dynamics
Finer Aspects of Reeb Dynamics and Topology

Lecture 2. Analytical Tools
A Priori Estimates
Bubbling-off Analysis
Behaviour near a Puncture

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