By Michèle Audin, Mihai Damian
This publication is an creation to fashionable tools of symplectic topology. it's dedicated to explaining the answer of an incredible 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 way of the size of the homology of the underlying manifold.
The first half is a radical advent 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 lined within the moment half. Floer homology is an infinite-dimensional analogue of Morse homology. Its involvement has been the most 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 elaborate and indicate using extra subtle analytical equipment, all of that are defined during this moment part.
The 3 appendices current a couple of must haves in differential geometry, algebraic topology and analysis.
The publication originated in a graduate path given at Strasbourg college, and encompasses a huge diversity of figures and workouts. Morse conception and Floer Homology could be fairly worthwhile for graduate and postgraduate students.