A History of Algebraic and Differential Topology, 1900 - 1960

  • Authors
  • Jean Dieudonné

Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Simplicia1 Techniques and Homology

    1. Front Matter
      Pages 1-1
    2. Jean Dieudonné
      Pages 3-14
    3. Jean Dieudonné
      Pages 15-35
    4. Jean Dieudonné
      Pages 36-59
    5. Jean Dieudonné
      Pages 60-66
    6. Jean Dieudonné
      Pages 67-157
  3. The First Applications of Simplicia1 Methods and of Homology

    1. Front Matter
      Pages 1-1
    2. Jean Dieudonné
      Pages 161-166
    3. Jean Dieudonné
      Pages 167-181
    4. Jean Dieudonné
      Pages 182-196
    5. Jean Dieudonné
      Pages 197-203
    6. Jean Dieudonné
      Pages 204-213
    7. Jean Dieudonné
      Pages 214-231
    8. Jean Dieudonné
      Pages 232-248
  4. Homotopy and its Relation to Homology

    1. Front Matter
      Pages 1-1
    2. Jean Dieudonné
      Pages 273-292
    3. Jean Dieudonné
      Pages 293-310

About this book

Introduction

Since the early part of the 20th century, topology has gradually spread to many other branches of mathematics, and this book demonstrates how the subject continues to play a central role in the field. Written by a world-renowned mathematician, this classic text traces the history of algebraic topology beginning with its creation in the early 1900s and describes in detail the important theories that were discovered before 1960. Through the work of Poincaré, de Rham, Cartan, Hureqicz, and many others, this historical book also focuses on the emergence of new ideas and methods that have led 21st-century mathematicians towards new research directions.

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This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it!

—MathSciNet

[The author] traces the development of algebraic and differential topology from the innovative work by Poincaré at the turn of the century to the period around 1960. [He] has given a superb account of the growth of these fields.… The details are interwoven with the narrative in a very pleasant fashion.… [The author] has previous written histories of functional analysis and of algebraic geometry, but neither book was on such a grand scale as this one. He has made it possible to trace the important steps in the growth of algebraic and differential topology, and to admire the hard work and major advances made by the founders.

—Zentralblatt MATH

Keywords

Algebraic topology Fundamental group History of Mathematics Homotopy Topology algebra calculus cohomology fibrations geometry homology homotopy theory mathematics proof theorem

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4907-4
  • Copyright Information Birkhäuser Boston 2009
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4906-7
  • Online ISBN 978-0-8176-4907-4
  • Series Print ISSN 2197-1803
  • Series Online ISSN 2197-1811
  • About this book