Introduction to Differential and Algebraic Topology

Borisovich, Yu. G.; Bliznyakov, N. M.; Fomenko, T. N.; Izrailevich, Y. A.

ISBN 10: 9048145589 / ISBN 13: 9789048145584

Edité par Springer, 2010

A propos de cet article

N° de réf. du vendeur 11865968-n

Détails bibliographiques

• Titre: Introduction to Differential and Algebraic Topology
• Éditeur: Springer
• Date de parution: 2010
• Langue: anglais
• ISBN à 10 chiffres: 9048145589
• ISBN à 13 chiffres: 9789048145584
• Reliure: Couverture souple
• État de l'article: New

A propos de ce titre

Synopsis

Topology as a subject, in our opinion, plays a central role in university education. It is not really possible to design courses in differential geometry, mathematical analysis, differential equations, mechanics, functional analysis that correspond to the temporary state of these disciplines without involving topological concepts. Therefore, it is essential to acquaint students with topo- logical research methods already in the first university courses. This textbook is one possible version of an introductory course in topo- logy and elements of differential geometry, and it absolutely reflects both the authors' personal preferences and experience as lecturers and researchers. It deals with those areas of topology and geometry that are most closely related to fundamental courses in general mathematics. The educational material leaves a lecturer a free choice in designing his own course or his own seminar. We draw attention to a number of particularities in our book. The first chap- ter, according to the authors' intention, should acquaint readers with topolo- gical problems and concepts which arise from problems in geometry, analysis, and physics. Here, general topology (Ch. 2) is presented by introducing con- structions, for example, related to the concept of quotient spaces, much earlier than various other notions of general topology thus making it possible for students to study important examples of manifolds (two-dimensional surfaces, projective spaces, orbit spaces, etc.) as topological spaces, immediately.

Présentation de l'éditeur

This Introduction to Topology, which is a thoroughly revised, extensively rewritten, second edition of the work first published in Russian in 1980, is a primary manual of topology. It contains the basic concepts and theorems of general topology and homotopy theory, the classification of two-dimensional surfaces, an outline of smooth manifold theory and mappings of smooth manifolds. Elements of Morse and homology theory, with their application to fixed points, are also included. Finally, the role of topology in mathematical analysis, geometry, mechanics and differential equations is illustrated.
Introduction to Topology contains many attractive illustrations drawn by A. T. Frenko, which, while forming an integral part of the book, also reflect the visual and philosophical aspects of modern topology. Each chapter ends with a review of the recommended literature.
Audience: Researchers and graduate students whose work involves the application of topology, homotopy and homology theories.