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An Introduction to Algebraic Topology

  • Joseph J. Rotman

Part of the Graduate Texts in Mathematics book series (GTM, volume 119)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Joseph J. Rotman
    Pages 1-13
  3. Joseph J. Rotman
    Pages 14-30
  4. Joseph J. Rotman
    Pages 31-38
  5. Joseph J. Rotman
    Pages 39-56
  6. Joseph J. Rotman
    Pages 57-85
  7. Joseph J. Rotman
    Pages 86-105
  8. Joseph J. Rotman
    Pages 106-130
  9. Joseph J. Rotman
    Pages 131-179
  10. Joseph J. Rotman
    Pages 180-227
  11. Joseph J. Rotman
    Pages 228-271
  12. Joseph J. Rotman
    Pages 272-311
  13. Joseph J. Rotman
    Pages 312-372
  14. Joseph J. Rotman
    Pages 373-418
  15. Back Matter
    Pages 419-437

About this book

Introduction

There is a canard that every textbook of algebraic topology either ends with the definition of the Klein bottle or is a personal communication to J. H. C. Whitehead. Of course, this is false, as a glance at the books of Hilton and Wylie, Maunder, Munkres, and Schubert reveals. Still, the canard does reflect some truth. Too often one finds too much generality and too little attention to details. There are two types of obstacle for the student learning algebraic topology. The first is the formidable array of new techniques (e. g. , most students know very little homological algebra); the second obstacle is that the basic defini­ tions have been so abstracted that their geometric or analytic origins have been obscured. I have tried to overcome these barriers. In the first instance, new definitions are introduced only when needed (e. g. , homology with coeffi­ cients and cohomology are deferred until after the Eilenberg-Steenrod axioms have been verified for the three homology theories we treat-singular, sim­ plicial, and cellular). Moreover, many exercises are given to help the reader assimilate material. In the second instance, important definitions are often accompanied by an informal discussion describing their origins (e. g. , winding numbers are discussed before computing 1tl (Sl), Green's theorem occurs before defining homology, and differential forms appear before introducing cohomology). We assume that the reader has had a first course in point-set topology, but we do discuss quotient spaces, path connectedness, and function spaces.

Keywords

Algebraic topology CW complex Fundamental group Homotopy Homotopy group Hurewicz theorem Loop group cohomology cohomology group fibrations function space homology point set topology

Authors and affiliations

  • Joseph J. Rotman
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4576-6
  • Copyright Information Springer-Verlag New York 1988
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8930-2
  • Online ISBN 978-1-4612-4576-6
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site