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Lectures on Algebraic Topology
EMS Series of Lectures in Mathematics

Sergey V. Matveev (Chelyabinsk State University, Russia)

Lectures on Algebraic Topology

ISBN print 978-3-03719-023-4, ISBN online 978-3-03719-523-9
DOI 10.4171/023
May 2006, 106 pages, softcover, 17.0 x 24.0 cm.
28.00 Euro

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.

Further Information

Review in Zentralblatt MATH 1094.55001

Review in MR 2227522

MAA Reviews

EMS Review