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.
|Published (Last):||12 June 2013|
|PDF File Size:||18.76 Mb|
|ePub File Size:||18.2 Mb|
|Price:||Free* [*Free Regsitration Required]|
Skip to main content. A publication of the European Mathematical Society. See our librarian mavteev for additional eBook ordering options. Two features make the text different from the standard literature: 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.
Matveev S.V. Lectures on Algebraic Topology
Melnikov, Chelyabinskii gosudarstvennyi universitet, Chelyabinsk,9— It has the smallest known volume. Here follows an example of this: Corresponding member of Petrov academy of sciences and arts. Distributed within the Americas by the American Mathematical Society. Chelyabinsk State University, Chelyabinsk, Russia. That is, the exercises and computability. The book oon with homology theory, which is introduced from the geometric approach of simplicial homology.
The albebraic 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.
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.
Some of them are provided to encourage and puzzle the independent reader as well as to make them evaluate their knowledge. Starting with the definition of the fundamental group, its computation is described via the Van Kampen theorem applied in different situations. The author’s intention is to rely on the geometric approach by appealing to the reader’s own intuition to help understanding. This book provides an introduction to the basic concepts and methods of algebraic topology for the beginner.
Basic and classical properties of simplicial homology together with some applications are then presented.
Lectures on Algebraic Topology
Second, the book contains many exercises, all of which are supplied with hints or solutions. Melnikov, Chelyabinskii gosudarstvennyi universitet, Chelyabinsk,38— But, as mentioned above, all of this follows from a quick first look at the book under review.
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. 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.
Citations in Web of Science: Publication Month and Year: 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. UrO RAN, 23no. 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.
In fact, whenever it is possible within the text, results and proofs are presented through a geometric vision and intuition. 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.
Rashevskii seminar on tensor and vector analysis with applications in geometry, mechanics and physics October 8, 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.
Matematika, mekhanika, informatika2 8— The numerous algebraicc in the text also serve this purpose. Finally, this text could also be of use for the expert from a teaching point of view. Rosebrock, Cambridge University Press, Cambridge,— The theory of elementary moves on special polyhedra is elaborated. Please switch it on to enable full functionality of the website.
The chapter also contains the Lefschetz fixed point theorem, a brief introduction to homology with coefficients, and a quick description of some elements of cohomology theory.
Having said that, there are two more aspects of the text that should be remarked upon, as the author gives them special attention. Lectures on Algebraic Topology Share this page.
Lectures on Algebraic Topology
Ordering on the AMS Bookstore is limited to individuals for personal use only. This makes the book suitable for both classroom use and for independent study.
In fact the whole book is scattered with many exercises of differing scales of difficulty and whose purposes vary. Algebraic topology is the study of the global properties of spaces by means of algebra. Libraries and resellers, please contact cust-serv ams.
Matveev S.V. Lectures on Algebraic Topology [PDF] – Все для студента
Then, the author introduces cellular homology and highlights the computational properties of this approach. Graduate students and research mathematicians interested in geometry and topology. 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.
The mathematical beginner, perhaps an undergraduate, will find a very intuitive and geometrical, yet formal and rigorous, approach to homology theory. Topologh 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.