Item Details
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 1periodic trajectories of a nondegenerate 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 infinitedimensional 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, 01725939
 Universitext. 01725939
 Technical Details

 Access in Virgo Classic
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LEADER 02872cam a2200445Ii 4500001 u6189625003 SIRSI005 20140128151659.0008 140110s2014 enka b 001 0 eng da 9781447154952 q Springer q paperbacka 1447154959 q Springer q paperbacka 9782759807048 q EDP Sciences q paperbacka 2759807045 q EDP Sciences q paperbackz 9781447154969 (online)a (Sirsi) o868017478a (OCoLC)868017478a OHX b eng c OHX d OCLCO d ZWZ d IL4I4a QA331 b .A9313 2014a Audin, Michèle.a Theorie de Morse et homologie de Floer l Englisha Morse theory and Floer homology / c Michele Audin, Mihai Damian ; translated by Reinie Erne.a London ; Heidelberg : b Springer, c 2014.a xiv, 596 pages : b illustrations ; c 24 cm.a text b txt 2 rdacontenta unmediated b n 2 rdamediaa volume b nc 2 rdacarriera Universitext, x 01725939a Textbook for graduates.a Includes bibliographical references and index.a 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 1periodic trajectories of a nondegenerate 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 infinitedimensional 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.a Morse theory.a Floer homology.a Damian, Iulian Mihai.z 9781447154969 (online)w (GyWOH)har130600080a Universitext. x 01725939a Z0 b VA@a 8a QA331 .A9313 2014 w LC i X031623920 l STACKS m MATH t BOOK
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QA331 .A9313 2014 