Morse Theory and Floer Homology

• Main Authors: Audin, Michèle (Author), Damian, Mihai (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London : Imprint: Springer, 2014.
• Series: Universitext,
• Subjects: Mathematics.; Geometry.; Differential geometry.; Algebraic topology.; Manifolds (Mathematics).; Complex manifolds.; Differential Geometry.; Algebraic Topology.; Manifolds and Cell Complexes (incl. Diff.Topology).

This book is an introduction to modern methods of symplectic topology. It is devoted to explaining the solution of an important problem originating from classical mechanics: the 'Arnold conjecture', which asserts that the number of 1-periodic trajectories of a non-degenerate Hamiltonian sy...

Table of Contents:

• Introduction to Part I
• Morse Functions
• Pseudo-Gradients
• The Morse Complex
• Morse Homology, Applications
• Introduction to Part II
• What You Need To Know About Symplectic Geometry
• The Arnold Conjecture and the Floer Equation
• The Maslov Index
• Linearization and Transversality
• Spaces of Trajectories
• From Floer To Morse
• Floer Homology: Invariance
• Elliptic Regularity
• Technical Lemmas
• Exercises for the Second Part
• Appendices: What You Need to Know to Read This Book.