Morse Theory and Floer Homology / by Michèle Audin, Mihai Damian.

Format:

Book

Author/Creator:

Audin, Michèle, Author.

Damian, Mihai, Author.

Series:

Universitext, 2191-6675

Language:

English

Subjects (All):

Geometry.

Geometry, Differential.

Algebraic topology.

Manifolds (Mathematics).

Differential Geometry.

Algebraic Topology.

Manifolds and Cell Complexes.

Local Subjects:

Geometry.

Differential Geometry.

Algebraic Topology.

Manifolds and Cell Complexes.

Physical Description:

1 online resource (595 p.)

Edition:

1st ed. 2014.

Place of Publication:

London : Springer London : Imprint: Springer, 2014.

Language Note:

English

Summary:

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 system is bounded below by the dimension of the homology of the underlying manifold. The first part is a thorough introduction to Morse theory, a fundamental tool of differential topology. It defines the Morse complex and the Morse homology, and develops some of their applications. Morse homology also serves a simple model for Floer homology, which is covered in the second part. Floer homology is an infinite-dimensional analogue of Morse homology. Its involvement has been crucial in the recent achievements in symplectic geometry and in particular in the proof of the Arnold conjecture. The building blocks of Floer homology are more intricate and imply the use of more sophisticated analytical methods, all of which are explained in this second part. The three appendices present a few prerequisites in differential geometry, algebraic topology and analysis. The book originated in a graduate course given at Strasbourg University, and contains a large range of figures and exercises. Morse Theory and Floer Homology will be particularly helpful for graduate and postgraduate students.

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.

Notes:

Description based upon print version of record.

Description based on publisher supplied metadata and other sources.

ISBN:

1-4471-5496-7

OCLC:

864875003