An invitation to Morse theory / Liviu I. Nicolaescu

The first part of the book lays foundations of Morse theory. Here the author introduces the basic notions, describes the main properties of Morse functions and proves the main technical theorems. This parts of the book treats Morse inequalities, Morse-Smale dynamics, Morse-Floer theory, Morse-Bott theory, as well as elements of the Lusternik-Schnirelamann theory. The presentation contains many pictures and interesting examples. As one of the examples the author analyzes Morse functions arising in robotics in the theory of the robot arm and in other mechanisms. The second part of the book is devoted to applications. These include a number of traditional applications such as computation of cohomology of complex Grassmannians and the Lefschetz hyperplane section theorem. Additionally, the author studies here some more recent and advanced topics: symplectic manifolds and Hamiltonian flows, moment maps and the equivariant localization. The last part of the book describes basics of the Picard-Lefschetz theory. The exposition contains complete proofs of the local and global Picard-Lefschetz formulae and applications of these results to the topology of algebraic manifolds. The concluding chapter contains many interesting exercises and their solutions. The book will be useful for mathematicians of various levels, including graduate students and researchers. (Zentralblatt)

Bibliogr. p. [233]-235. Index