Universitext

Morse Theory and Floer Homology

Authors: Audin, Michèle, Damian, Mihai

  • 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
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eBook $69.99
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  • ISBN 978-1-4471-5496-9
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Softcover $89.99
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  • ISBN 978-1-4471-5495-2
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About this Textbook

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.

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)


Table of contents (14 chapters)

  • Morse Functions

    Audin, Michèle (et al.)

    Pages 7-21

  • Pseudo-Gradients

    Audin, Michèle (et al.)

    Pages 23-52

  • The Morse Complex

    Audin, Michèle (et al.)

    Pages 53-78

  • Morse Homology, Applications

    Audin, Michèle (et al.)

    Pages 79-123

  • What You Need to Know About Symplectic Geometry

    Audin, Michèle (et al.)

    Pages 129-149

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4471-5496-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-1-4471-5495-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Morse Theory and Floer Homology
Authors
Series Title
Universitext
Copyright
2014
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
Distribution Rights
Distribution rights for France: EDP Sciences, Les Ulis Cedex A, France
eBook ISBN
978-1-4471-5496-9
DOI
10.1007/978-1-4471-5496-9
Softcover ISBN
978-1-4471-5495-2
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XIV, 596
Number of Illustrations and Tables
114 b/w illustrations
Additional Information
Original French edition published by EDP Sciences, Les Ulis Cedex A, France, 2010
Topics