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Introduction to Differential and Algebraic Topology

  • Yuri G. Borisovich
  • Nikolai M. Bliznyakov
  • Tatyana N. Fomenko
  • Yakov A. Izrailevich

Part of the Kluwer Texts in the Mathematical Sciences book series (TMS, volume 9)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Yuri G. Borisovich, Nikolai M. Bliznyakov, Tatyana N. Fomenko, Yakov A. Izrailevich
    Pages 1-59
  3. Yuri G. Borisovich, Nikolai M. Bliznyakov, Tatyana N. Fomenko, Yakov A. Izrailevich
    Pages 61-160
  4. Yuri G. Borisovich, Nikolai M. Bliznyakov, Tatyana N. Fomenko, Yakov A. Izrailevich
    Pages 161-215
  5. Yuri G. Borisovich, Nikolai M. Bliznyakov, Tatyana N. Fomenko, Yakov A. Izrailevich
    Pages 217-386
  6. Yuri G. Borisovich, Nikolai M. Bliznyakov, Tatyana N. Fomenko, Yakov A. Izrailevich
    Pages 387-476
  7. Back Matter
    Pages 477-493

About this book

Introduction

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.

Keywords

Algebraic topology Homotopy homology homotopy theory manifold topology

Authors and affiliations

  • Yuri G. Borisovich
    • 1
  • Nikolai M. Bliznyakov
    • 1
  • Tatyana N. Fomenko
    • 2
  • Yakov A. Izrailevich
    • 1
  1. 1.Voronezh State UniversityVoronezhRussia
  2. 2.Moscow Institute of Steel and AlloysMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-1959-9
  • Copyright Information Springer Science+Business Media B.V. 1995
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4558-4
  • Online ISBN 978-94-017-1959-9
  • Series Print ISSN 0927-4529
  • Buy this book on publisher's site