Elements of Homotopy Theory

  • George W. Whitehead

Part of the Graduate Texts in Mathematics book series (GTM, volume 61)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. George W. Whitehead
    Pages 1-45
  3. George W. Whitehead
    Pages 46-95
  4. George W. Whitehead
    Pages 96-156
  5. George W. Whitehead
    Pages 157-208
  6. George W. Whitehead
    Pages 209-254
  7. George W. Whitehead
    Pages 255-313
  8. George W. Whitehead
    Pages 314-370
  9. George W. Whitehead
    Pages 371-414
  10. George W. Whitehead
    Pages 415-455
  11. George W. Whitehead
    Pages 456-487
  12. George W. Whitehead
    Pages 488-541
  13. George W. Whitehead
    Pages 542-601
  14. George W. Whitehead
    Pages 602-671
  15. Back Matter
    Pages 673-746

About this book


As the title suggests, this book is concerned with the elementary portion of the subject of homotopy theory. It is assumed that the reader is familiar with the fundamental group and with singular homology theory, including the Universal Coefficient and Kiinneth Theorems. Some acquaintance with manifolds and Poincare duality is desirable, but not essential. Anyone who has taught a course in algebraic topology is familiar with the fact that a formidable amount of technical machinery must be introduced and mastered before the simplest applications can be made. This phenomenon is also observable in the more advanced parts of the subject. I have attempted to short-circuit it by making maximal use of elementary methods. This approach entails a leisurely exposition in which brevity and perhaps elegance are sacrificed in favor of concreteness and ease of application. It is my hope that this approach will make homotopy theory accessible to workers in a wide range of other subjects-subjects in which its impact is beginning to be felt. It is a consequence of this approach that the order of development is to a certain extent historical. Indeed, if the order in which the results presented here does not strictly correspond to that in which they were discovered, it nevertheless does correspond to an order in which they might have been discovered had those of us who were working in the area been a little more perspicacious.


Base Calc Characteristic class Elements Excision theorem Fundamental group Homotopie Homotopy Homotopy group Hurewicz theorem Maxima algebra computation group time

Authors and affiliations

  • George W. Whitehead
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York 1978
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6320-3
  • Online ISBN 978-1-4612-6318-0
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site