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A History of Algebraic and Differential Topology 1900-1960 (Hardback)

A History of Algebraic and Differential Topology 1900-1960 (Hardback)

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Condition

VERY GOOD: The book is in very good condition, showing only the slightest signs of use and wear (namely, slightly bent cover corners). The pages are clean and the binding is tight. It is printed on acid-free paper.

Product Details

From the back cover: "In its first thirty years the field [of algebraic topology] seemed limited to applications in algebraic geometry, but this changed dramatically in the 1930s with the creation of differential topology by Georges De Rham and Elie Cartan and of homotopy theory by Witold Hurewicz and Heinz Hopf. The influence of topology began to spread to more and more branches as it gradually took on a central place in mathematics.
"Written by a world-renowned mathematician, this book will make exciting reading for anyone working with topology."

BRIEF CONTENTS

  • Preface
  • Notations
  • PART 1. Simplicial Techniques and Homology
    • Introduction
    • Chapter I. The Work of Poincaré
    • Chapter II. The Build-Up of "Classical" Homology
    • Chapter III. The Beginnings of Differential Topology
    • Chapter IV. The Various Homology and Cohomology Theories
  • PART 2. The First Applications of Simplicial Methods and of Homology
    • Introduction
    • Chapter I. The Concept of Degree
    • Chapter II. Dimension Theory and Separation Theorems
    • Chapter III. Fixed Points
    • Chapter IV. Local Homological Properties
    • Chapter V. Quotient Spaces and Their Homology
    • Chapter VI. Homology of Groups and Homogeneous Spaces
    • Chapter VII. Applications of Homology to Geometry and Analysis
  • PART 3. Homotopy and its Relation to Homology
    • Introduction
    • Chapter I. Fundamental Group and Covering Spaces
    • Chapter II. Elementary Notation and Early Results in Homotopy Theory
    • Chapter III. Fibrations
    • Chapter IV. Homology of Fibrations
    • Chapter V. Sophisticated Relations between Homotopy and Homology
    • Chapter VI. Cohomology Operations
    • Chapter VII. Generalized Homology and Cohomology
  • Bibliography
  • Index of Cited Names
  • Subject Index
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AUTHOR: Dieudonné;Jean
PUBLISHER: Birkhauser
ISBN-13: 9780817633882
ISBN-10: 081763388X
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A History of Algebraic and Differential Topology 1900-1960 (Hardback)
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