A History of Algebraic and Differential Topology, 1900 - 1960

Authors:

ISBN: 978-0-8176-4906-7 (Print) 978-0-8176-4907-4 (Online)

Table of contents (23 chapters)

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  1. Front Matter

    Pages i-xxii

  2. Simplicia1 Techniques and Homology

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 3-14

      Introduction

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      Book Chapter

      Pages 15-35

      The Work of Poincaré

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      Book Chapter

      Pages 36-59

      The Build-Up of “Classical” Homology

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      Book Chapter

      Pages 60-66

      The Beginnings of Differential Topology

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      Book Chapter

      Pages 67-157

      The Various Homology and Cohomology Theories

  3. The First Applications of Simplicia1 Methods and of Homology

    1. Front Matter

      Pages 1-1

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      Book Chapter

      Pages 161-166

      Introduction

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      Book Chapter

      Pages 167-181

      The Concept of Degree

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      Book Chapter

      Pages 182-196

      Dimension Theory and Separation Theorems

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      Book Chapter

      Pages 197-203

      Fixed Points

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      Book Chapter

      Pages 204-213

      Local Homological Properties

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      Book Chapter

      Pages 214-231

      Quotient Spaces and Their Homology

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      Book Chapter

      Pages 232-248

      Homolagy of Groups and Homogeneous Spaces

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      Book Chapter

      Pages 249-269

      Applications of Homology to Geometry and Analysis

  4. Homotopy and its Relution to Homology

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 273-292

      Introduction

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      Book Chapter

      Pages 293-310

      Fundamental Group and Covering Spaces

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      Book Chapter

      Pages 311-384

      Elementary Notions and Early Results in Homotopy Theory

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      Book Chapter

      Pages 385-420

      Fibrations

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      Book Chapter

      Pages 421-452

      Homology of Fibrations

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      Book Chapter

      Pages 453-509

      Sophisticated Relations between Homotopy and Homology

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      Book Chapter

      Pages 510-554

      Cohomology Operations

  5. Back Matter

    Pages 1-37

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