Morse Theory and Floer Homology
, "Morse Theory and Floer Homology "
English | ISBN: 1447154959 | 2014 | 610 pages | EPUB | 9 MB
English | ISBN: 1447154959 | 2014 | 610 pages | EPUB | 9 MB
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.
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