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Morse Theory and Floer Homology

Michele Audin, Mihai Damian ; translated by Reinie Erne
Format
Book
Published
London ; Heidelberg : Springer, 2014.
Language
English
Uniform Title
Theorie de Morse et homologie de Floer English
Series
Universitext
ISBN
9781447154952, 1447154959, 9782759807048, 2759807045, 9781447154969 (online)
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.
Description
xiv, 596 pages : illustrations ; 24 cm.
Notes
  • Textbook for graduates.
  • Includes bibliographical references and index.
Series Statement
Universitext, 0172-5939
Universitext. 0172-5939
Technical Details
  • Access in Virgo Classic
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