Morse Theory and Floer Homology

The book "Morse Theory and Floer Homology" offers a comprehensive introduction to modern methods in symplectic topology and addresses a central problem in classical mechanics, the Arnold conjecture. This conjecture states that the number of 1-periodic trajectories of a non-degenerate Hamiltonian system is bounded from below by the dimension of the homology of the underlying manifold. The first part of the book is dedicated to Morse theory, a fundamental tool in differential topology, and defines the Morse complex as well as Morse homology and its applications. The second part deals with Floer homology, which serves as an infinite-dimensional extension of Morse homology and is crucial for advancements in symplectic geometry. The book also includes three appendices that present some prerequisites in differential geometry, algebraic topology, and analysis. It is particularly aimed at graduate and postgraduate students and contains numerous illustrations and exercises.