Lectures on Algebraic Topology For the graduate student, or the outsider to algebraic topology with some mathematical sergey v. matveev. The book under review, Lectures on Algebraic Topology, by Sergey V. Matveev, has the additional benefit of being expressly geared toward the. Sergey V. Matveev. Lectures on. Algebraic Topology. Translated by Ekaterina Pervova. European ^AAathematical vjbciety.

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Matematika, mekhanika, informatika, no. Lectures on Algebraic Topology Share this page.

Please switch it on to enable full functionality of the website. Print Price 2 Label: 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. Matematika, mekhanika, informatika2 8— Basic and classical properties of simplicial homology together with some applications are then presented.

The mathematical beginner, perhaps an undergraduate, will find a very intuitive and geometrical, yet formal and rigorous, approach to homology theory. 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.

Some of them are provided to encourage and puzzle the independent reader as well as to make them evaluate their knowledge. Second, the book contains many exercises, all of which are supplied with hints or solutions.

Lectures on Algebraic Topology

The book begins with homology theory, which is introduced from the geometric approach of simplicial homology. Here follows an example of this:.

It has the smallest known volume. But, as mentioned above, all of this follows from a quick first look at the book under review. Libraries and resellers, please contact cust-serv ams. Tematicheskii sbornik nauchnykh trudov, Chelyabinskii politekhnicheskii institut, Chelyabinsk,79— The basics of homotopy theory are then presented in very brief terms. Lectures on Algebraic Topology At a first glance, this nice, short book is comparable to other brief texts of a similar vein. Others are included to fill gaps left on purpose either to complete proofs of stated theorems or to establish results needed to make the book self-contained.


After a careful reading, though, this short piece reveals many insights from which different readers may benefit. The chapter also contains the Pectures fixed point theorem, algdbraic brief introduction to homology with coefficients, and a quick description of some elements of letcures theory. Graduate students and research mathematicians interested in geometry and topology. 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.

See our librarian page for additional eBook ordering options. Finally, this text could also be of mztveev for the expert from a teaching point of view.

It presents elements of both homology theory and homotopy theory, and includes various applications. Citations in Web of Science: This book provides an introduction to the basic concepts and methods of algebraic topology for the beginner. Then, the author introduces cellular homology and highlights the computational properties of this approach. Zlgebraic am sure that any experienced mathematician could find topoloyy new ways and tips, at least of an expository nature, of presenting these classical topics in the classroom.

The numerous illustrations in the text also serve this purpose.

Lectures on Algebraic Topology : Sergey V. Matveev :

The chapter is completed with a compendium of the basic properties of covering spaces. A publication of the European Mathematical Society. Author s Product display: 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. Distributed within the Americas by the American Mathematical Matveeb. Print Price 1 Label: Join our email list.


Lectures on Algebraic Topology

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. Corresponding oh of Petrov academy of sciences and arts.

On the other hand, lectuures computability, by giving explicit and far from complicated algorithms the author points out aalgebraic homology groups and fundamental groups can be explicitly calculated for many spaces found in nature. Here follows an example of this: 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.

Skip to main content. 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. The theory of elementary moves on special polyhedra is elaborated. Starting with the definition of the fundamental group, its computation is described katveev the Van Kampen theorem applied in different situations.

Rosebrock, Cambridge University Press, Cambridge,topoloty Melnikov, Chelyabinskii gosudarstvennyi universitet, Chelyabinsk,16— On one hand, some aspects of algebraic topology are presented in a not commonly used approach for instance, the computation of the fundamental group of the complement of some knots.

For the graduate student, tolology the outsider to algebraic topology with some mathematical knowledge and with interests in other branches, this book is also of help.

Papadopoulos, European Mathematical Society, Zurich,— In fact the whole book is scattered with many exercises of differing scales of difficulty and whose purposes vary.

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