1549055384-Symplectic_Geometry_and_Topology__Eliashberg_

CONTENTS

Motivation

Seiberg-Witten and Pseudoholomorphic Curves

Definition of the Gromov Invariant

Bibliography

Dietmar Salamon, Lectures on Floer Homology
Introduction

Lecture 1. Symplectic Fixed Points and Morse Theory
The Arnold Conjecture
The Monotonicity Condition
The Morse-Smale-Witten Complex
Symplectic Action
Connecting Orbits
Moduli Spaces

Lecture 2. Fredholm Theory
Fredholm Operators
The Linearized Operator
LP-Estimates
The Conley-Zehnder Index
The Spectral Flow
Transversali ty
Exponential Convergence

Lecture 3. Floer Homology

Compactness

Floer Homology

Floer's Gluing Theorem

Invariance of Floer Homology

A Natural Isomorphism

Calabi-Yau Manifolds

N ovikov Rings

Floer Homology Revisited

Lecture 4. Gromov Compactness and Stable Maps
Bubbling
Soft Rescaling
Stable Maps
Deligne-Mumford Compactification

Lecture 5. Multi-Valued Perturbations
J-Holomorphic Spheres with Negative Chern Number
Multi-valued Perturbations
Local Slices
Branched Moduli Spaces
Perturbations and Stable Maps
Perturbations and Marked Points
Perturbations and Stable Maps
Compatibility

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