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Topology and Geometry

  • Glen E. Bredon

Part of the Graduate Texts in Mathematics book series (GTM, volume 139)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Glen E. Bredon
    Pages 1-62
  3. Glen E. Bredon
    Pages 63-126
  4. Glen E. Bredon
    Pages 127-167
  5. Glen E. Bredon
    Pages 168-259
  6. Glen E. Bredon
    Pages 260-314
  7. Glen E. Bredon
    Pages 315-429
  8. Glen E. Bredon
    Pages 430-517
  9. Back Matter
    Pages 519-561

About this book

Introduction

The golden age of mathematics-that was not the age of Euclid, it is ours. C. J. KEYSER This time of writing is the hundredth anniversary of the publication (1892) of Poincare's first note on topology, which arguably marks the beginning of the subject of algebraic, or "combinatorial," topology. There was earlier scattered work by Euler, Listing (who coined the word "topology"), Mobius and his band, Riemann, Klein, and Betti. Indeed, even as early as 1679, Leibniz indicated the desirability of creating a geometry of the topological type. The establishment of topology (or "analysis situs" as it was often called at the time) as a coherent theory, however, belongs to Poincare. Curiously, the beginning of general topology, also called "point set topology," dates fourteen years later when Frechet published the first abstract treatment of the subject in 1906. Since the beginning of time, or at least the era of Archimedes, smooth manifolds (curves, surfaces, mechanical configurations, the universe) have been a central focus in mathematics. They have always been at the core of interest in topology. After the seminal work of Milnor, Smale, and many others, in the last half of this century, the topological aspects of smooth manifolds, as distinct from the differential geometric aspects, became a subject in its own right.

Keywords

Algebraic topology Fundamental group Homotopy cohomology homology homotopy theory

Authors and affiliations

  • Glen E. Bredon
    • 1
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-6848-0
  • Copyright Information Springer-Verlag New York 1993
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3103-0
  • Online ISBN 978-1-4757-6848-0
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site