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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Ordering on the AMS Bookstore is limited to individuals for personal use only. 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.
But, as mentioned above, all of this follows from a quick first look at the book under review.
Here follows an example of toppology Melnikov, Chelyabinskii gosudarstvennyi universitet, Chelyabinsk,9— UrO RAN, 23no. Papadopoulos, European Mathematical Society, Zurich,— Melnikov, Chelyabinskii gosudarstvennyi universitet, Chelyabinsk,38— The book begins with homology theory, which is introduced from the geometric approach of simplicial homology.
Distributed within the Americas by the American Mathematical Society.
Review: Lectures on Algebraic Topology | EMS
On the other hand, concerning computability, by giving explicit and far from complicated algorithms the author points out algdbraic homology groups and fundamental groups can be explicitly calculated for many spaces found in nature. Publication Month and Year: Decompositions of global knots S.
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. Some of them are provided to encourage and puzzle the independent reader as well as to make them evaluate their knowledge.
Matveev S.V. Lectures on Algebraic Topology
Second, the book contains many exercises, all of which are supplied with hints or solutions. Skip to main content. Join our email altebraic. Lectures on Algebraic Topology Share this page.
Lectures on Algebraic Topology
In fact, whenever it is possible within the text, results and proofs are presented through a geometric vision and intuition. Melnikov, Chelyabinskii gosudarstvennyi universitet, Chelyabinsk,16— Print Price 1 Label: A publication of the European Mathematical Society. The topooogy of homotopy theory are then presented in very brief terms.
In fact the whole book is scattered with many exercises of differing scales of difficulty and whose purposes vary.
Lectures on Algebraic Topology
Corresponding member of Petrov academy of sciences and arts. The mathematical beginner, perhaps an undergraduate, will find a very intuitive and geometrical, yet formal and rigorous, approach to homology theory. Algebraic topology is the study of the global properties of spaces by means of algebra.
Rosebrock, Cambridge University Press, Cambridge,— Tematicheskii sbornik nauchnykh trudov, Chelyabinskii politekhnicheskii institut, Chelyabinsk,79— Graduate students and research mathematicians otpology in geometry and topology.
Citations in Web of Science: Lectures on Algebraic Topology At a first glance, this nice, short book is comparable to other brief texts of a similar vein.
Two features make the text different from the standard literature: Finally, this text could also be of use for the expert from a teaching point of view. After a careful reading, though, this short piece reveals many insights from which different readers may benefit.