Introduction to the theory of Morse. A closed presentation with the necessary chapters from topology and geometry. 2nd edition. Postnikov M.M.

This book contains a detailed presentation of the basics of variational calculus in the direction laid down by the work of the fruit drink. The first three chapters are devoted to topologies: the necessary information is presented (in particular, it was in this book that for the first time in the educational literature the definition and the basic properties of cell breakdown were set out). The following chapters are devoted to smooth diversity, tensor calculation, Riman geometry, etc. In the ninth, final, chapter, the main theorem of the theory of Morse is proved, describing the structure of the space of curves connecting two data points of complete Rimanov space; The simplest applications of the theory of fruit drinks to the topology and geometry of riman spaces are given. Each chapter has been suggested by a brief introduction to the review of its content.

The book is recommended for students of the Physical and Mathematics faculties of universities, graduate students, teachers, scientists.