EDP Sciences
20202609
eng
bookstore.edpsciences.com/65/9782759807048
03
01
EDP Sciences bookstore
03
9782759807048
15
9782759807048
BA
Universitext
<TitleType>01</TitleType>
<TitleText>Morse Theory and Floer Homology</TitleText>
1
A01
Michèle
Audinet
2
A01
Damian
Mihai
<p>Damian Mihai, maître de conférences à l'Université de Strasbourg, est spécialiste de géométrie et topologie symplectiques. (au moment de la parution de l'ouvrage)</p>
NED
1
01
eng
596
23
Mathematics
01
02
<p>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. </p> <p>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.</p> <p>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.</p> <p>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.</p>
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06
09
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.
04
03
01
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01
EDP Sciences
FR
04
20140201
01
1.0
mm
02
1.0
mm
EDP Sciences
01
20
02
02
73.84
EUR
S
5.50
69.99
3.85