Main Lectures on algebraic topology Lectures on algebraic topology Sergey V. Matveev 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.

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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. In fact the whole book mattveev scattered with many exercises of differing scales of difficulty and whose purposes vary.

Basic and classical topologu of simplicial homology together with some applications are then presented. Corresponding member of Petrov academy of sciences and arts. On one hand, some aspects of algebraic topology are presented in a not commonly used approach for instance, the tipology of the fundamental group of the complement of some knots.

Lectures on Algebraic Topology On the other hand, concerning computability, by giving explicit and far from complicated algorithms the author points out that homology groups and fundamental groups can be explicitly calculated for many spaces found in nature. Its main purpose is to introduce the reader to the basics of algebraic topology and in particular to homology theory and its applications which is described in depth — about three-quarters of the book is devoted to it and homotopy theory.

Lectures on Algebraic Topology Share this page. Print Price 1 Label: Melnikov, Chelyabinskii gosudarstvennyi universitet, Chelyabinsk,9— Citations in Web of Science: I am sure that any experienced mathematician could find here new ways and tips, at least of an expository nature, of presenting these classical topics in the classroom.

UrO RAN, 23no. This book provides an introduction to the basic concepts and methods of algebraic topology for the beginner. Lectures on Algebraic Topology Matematika, mekhanika, informatika, no. Then, the author introduces cellular homology and highlights the computational properties of this approach. Starting with the definition of the fundamental group, its computation is described via the Van Kampen theorem applied in different situations. A publication of the European Mathematical Society.

The numerous illustrations in the text also serve this purpose. The mathematical beginner, perhaps an undergraduate, will find a very intuitive and geometrical, yet formal and rigorous, approach to homology theory.

Melnikov, Chelyabinskii gosudarstvennyi universitet, Chelyabinsk,38— Decompositions of global knots S. Chelyabinsk State University, Chelyabinsk, Russia. Author s Product display: Libraries and resellers, please contact cust-serv ams. The smooth and clear explanation at the beginning of the text of how the abstract concepts of categories and functors are going to be used later on, as well as the geometrical sketch of the proof of the uniqueness of homology theory on polyhedra and the introduction to cellular homology for computational purposes, are good examples of this attempt to bring non-trivial concepts to beginners.

A very short introduction to higher homotopy groups and the action on them by the fundamental group is then followed by an equally extensive presentation of the long exact sequence of a fibre bundle.

The chapter is completed with a compendium of the basic properties of covering spaces. The classical combinatorial difficulties to understanding simplicial homology a good example being the proof of the simplicial approximation theorem are overcome with a coherent, geometrical and logical exposition.

It presents elements of both homology theory and homotopy theory, and includes various applications. Here follows an example of this:. At a first glance, this nice, short book is comparable to other brief texts of a similar vein. Finally, this text could also be of use for the expert from a teaching point of view.

See our librarian page for additional eBook ordering options. The basics of homotopy theory are then presented in very brief terms. After a careful reading, though, this short piece reveals many insights from which different readers may benefit. After the introduction of the degree of a self map on a manifold, and with the few tools developed at that point, the author readily presents the homotopy classification of immersions of the circle into the plane and the fundamental theorem of algebra, and shows that a vector filed on the 2-sphere has a singular point.

On the other hand, the use of the basics of simplicial homology theory to attain deep results on more geometrical environments are given in the same geometrical but rigorous language. Persons: Matveev Sergei Vladimirovich Algebraic topology is the study of the global properties of spaces by means of algebra.

This makes the book suitable for both classroom use and for independent study. Here follows an example of this: Ordering on the AMS Bookstore is limited to topologt for personal use only. JavaScript is disabled in your browser. It is proved that the restriction of the Zeeman conjecture onto special polyhedra is equivalent to the union of the Poincare conjecture and the Andrews—Curtis conjecture. For the graduate student, or the outsider to algebraic topology with some mathematical knowledge and with interests in other branches, this book is also of help.

Having said that, there are two more aspects of the text that should be remarked upon, as the author gives them special attention. It has the smallest known volume. TOP 10 Related.

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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. In fact the whole book mattveev scattered with many exercises of differing scales of difficulty and whose purposes vary. Basic and classical topologu of simplicial homology together with some applications are then presented. Corresponding member of Petrov academy of sciences and arts. On one hand, some aspects of algebraic topology are presented in a not commonly used approach for instance, the tipology of the fundamental group of the complement of some knots.

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