Lectures on Algebraic Topology (EMS Series of Lectures in Mathematics) (EMS Series of Lectures in Mathematics)

Algebraic topology is the study of the global properties of spaces by means of algebra. It is an important branch of modern mathematics with a wide degree of applicability to other fields, including geometric topology, differential geometry, functional analysis, differential equations, algebraic geometry, number theory, and theoretical physics. This book provides an introduction to the basic concepts and methods of algebraic topology for the beginner. It presents elements of both homology theory and homotopy theory, and includes various applications. The author's intention is to rely on the geometric approach by appealing to the reader's own intuition to help understanding. The numerous illustrations in the text also serve this purpose. Two features make the text different from the standard literature: first, special attention is given to providing explicit algorithms for calculating the homology groups and for manipulating the fundamental groups. Second, the book contains many exercises, all of which are supplied with hints or solutions. This makes the book suitable for both classroom use and for independent study. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. One of the main parts of algebraic topology is homology theory, which is a functor from the category of topological spaces to the category of sequences of Abelian groups. Elements Of Homology Theory -- Elements Of Homotopy Theory. Sergey V. Matveev ; Translated By Ekaterina Pervova. Includes Bibliographical References (p. [95]) And Index.