By Michèle Audin,Mihai Damian
This booklet is an creation to fashionable equipment of symplectic topology. it truly is dedicated to explaining the answer of a huge challenge originating from classical mechanics: the 'Arnold conjecture', which asserts that the variety of 1-periodic trajectories of a non-degenerate Hamiltonian approach is bounded less than by means of the size of the homology of the underlying manifold.
The first half is an intensive creation to Morse idea, a basic software of differential topology. It defines the Morse complicated and the Morse homology, and develops a few of their applications.
Morse homology additionally serves an easy version for Floer homology, that's coated within the moment half. Floer homology is an infinite-dimensional analogue of Morse homology. Its involvement has been an important within the fresh achievements in symplectic geometry and specifically within the facts of the Arnold conjecture. The development blocks of Floer homology are extra problematic and indicate using extra subtle analytical equipment, all of that are defined during this moment part.
The 3 appendices current a number of necessities in differential geometry, algebraic topology and analysis.
The e-book originated in a graduate direction given at Strasbourg collage, and incorporates a huge variety of figures and workouts. Morse idea and Floer Homology might be relatively valuable for graduate and postgraduate students.
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Morse Theory and Floer Homology (Universitext) by Michèle Audin,Mihai Damian