Introduction to Differential and Algebraic Topology

1. Front Matter

   Pages i-ix

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2. First Notions of Topology

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

   Pages 1-59

3. General Topology

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

   Pages 61-160

4. Homotopy Theory

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

   Pages 161-215

5. Manifolds and Fiberings

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

   Pages 217-386

6. Homology Theory

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

   Pages 387-476

7. Back Matter

   Pages 477-493

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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.

• Algebraic topology
• Homotopy
• homology
• homotopy theory
• manifold
• topology

• Voronezh State University, Voronezh, Russia

  Yuri G. Borisovich, Nikolai M. Bliznyakov, Yakov A. Izrailevich

• Moscow Institute of Steel and Alloys, Moscow, Russia

  Tatyana N. Fomenko

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