EDP Sciences EDP Sciences EDP Sciences EDP Sciences

Morse Theory and Floer Homology

Collection: Universitext
february 2014
Paper book
1 x 1 format 596 pages In stock
73,84 €
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Presentation

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 as 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.

Compléments

Characteristics

Language(s): English

Audience(s): Extended public

Publisher: EDP Sciences

Edition: 1st edition

Collection: Universitext

Published: 1 february 2014

EAN13 Paper book: 9782759807048

Interior: Black & white

Format (in mm) Paper book: 1 x 1

Pages count Paper book: 596

Weight (in grammes): 1 (Paper book)