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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Lectures on Algebraic Topology
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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.
A publication of the European Mathematical Society.
Persons: Matveev Sergei Vladimirovich
Distributed within the Americas by the American Mathematical Society. Matematika, mekhanika, informatika, no.
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.
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 At a first glance, this nice, short to;ology is comparable to other brief texts of a similar vein.
See our librarian page for additional eBook ordering options. The numerous illustrations in the text also serve this purpose. Chelyabinsk State University, Chelyabinsk, Russia. Print Price 2 Label: UrO RAN, 23no. Matematika, mekhanika, informatika2 8— The book begins with homology theory, which is introduced from the o approach of simplicial homology. 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.
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. It presents elements of both homology theory and homotopy theory, and includes various applications. For the graduate student, or the outsider to algebraic topology with some mathematical knowledge and toppology interests in other branches, this book is also of help.
Review: Lectures on Algebraic Topology | EMS
Melnikov, Chelyabinskii gosudarstvennyi universitet, Chelyabinsk,38— Then, the author introduces cellular homology and highlights the computational properties of this approach. Skip to main content.
Lectures on Algebraic Topology Share this page. The chapter is completed with a compendium of the basic properties of covering spaces. Publication Month and Year: The basics of homotopy theory are then presented in very brief terms.
But, as mentioned above, all of this follows from a quick first look at the book under review. Papadopoulos, European Mathematical Society, Zurich,— After that, the axiomatic approach to homology theory is described together with a sketch of the proof of uniqueness of homology theory on polyhedra. In fact, whenever it is possible within the text, results and proofs are presented through a geometric vision and intuition.
Rosebrock, Cambridge University Press, Cambridge,— The theory of elementary moves on special polyhedra is elaborated.
Matveev S.V. Lectures on Algebraic Topology
In fact the whole book is scattered with many exercises of differing scales of difficulty and whose purposes vary. Finally, this text could also be of use for the expert from a teaching point of view. Here follows an example of this: