Overview
- Translation of the popular French textbook
- Provides a unified presentation of Morse theory and Floer homology that is unique in the English language
- Explains all the required background on symplectic geometry, differential geometry, algebraic topology and analysis
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
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About this book
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.
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Keywords
Table of contents (14 chapters)
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Front Matter
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Morse Theory
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Front Matter
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The Arnold Conjecture, Floer Homology
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Front Matter
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Back Matter
Reviews
From the book reviews:
“The present book is an excellent, detailed and self-contained introduction to Morse theory and Floer homology which makes both topics easily accessible to graduate or even advanced undergraduate students.” (Sonja Hohloch, Mathematical Reviews, August, 2014)
“Morse Theory and Floer Homology is a relatively high-level introduction to, and in fact a full account of, the extremely elegant and properly celebrated solution to the Arnol’d problem by the prodigious and tragic Andreas Floer … . the book is exceptionally well written. Indeed, this is a very good book on a beautiful and important subject and will richly repay those who take the time to work through it.” (Michael Berg, MAA Reviews, February, 2014)
Authors and Affiliations
Bibliographic Information
Book Title: Morse Theory and Floer Homology
Authors: Michèle Audin, Mihai Damian
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-4471-5496-9
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London Ltd., part of Springer Nature 2014
Softcover ISBN: 978-1-4471-5495-2Published: 17 December 2013
eBook ISBN: 978-1-4471-5496-9Published: 29 November 2013
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XIV, 596
Number of Illustrations: 114 b/w illustrations
Additional Information: Original French edition published by EDP Sciences, Les Ulis Cedex A, France, 2010
Topics: Geometry, Differential Geometry, Algebraic Topology, Manifolds and Cell Complexes (incl. Diff.Topology)