Title
Morse theory and Floer homology [electronic resource] / Michèle Audin, Mihai, Damain ; translated by Reinie Erné.
Uniform Title
Théorie de Morse et homologie de Floer. English
translation of (work) Théorie de Morse et homologie de Floer.
ISBN
9781447154969 electronic book
1447154967 electronic book
9781447154952
Published
London : Springer, 2014.
Language
English
Description
1 online resource (xiv, 596 pages) : illustrations.
Other Standard Identifiers
10.1007/978-1-4471-5496-9 doi
Call Number
QA331
Dewey Decimal Classification
515/.9
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.
Bibliography, etc. Note
Includes bibliographical references and indexes.
Access Note
Access limited to authorized users.
Source of Description
Description based on print version record.
Series
Universitext.
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.
