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Elements of Homotopy Theory

  • Textbook
  • © 1978

Overview

Authors:
  1. George W. Whitehead

    1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

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

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xxi
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  2. Introductory Notions

    • George W. Whitehead
    Pages 1-45

  3. CW-complexes

    • George W. Whitehead
    Pages 46-95

  4. Generalities on Homotopy Classes of Mappings

    • George W. Whitehead
    Pages 96-156

  5. Homotopy Groups

    • George W. Whitehead
    Pages 157-208

  6. Homotopy Theory of CW-complexes

    • George W. Whitehead
    Pages 209-254

  7. Homology with Local Coefficients

    • George W. Whitehead
    Pages 255-313

  8. Homology of Fibre Spaces: Elementary Theory

    • George W. Whitehead
    Pages 314-370

  9. The Homology Suspension

    • George W. Whitehead
    Pages 371-414

  10. Postnikov Systems

    • George W. Whitehead
    Pages 415-455

  11. On Mappings into Group-like Spaces

    • George W. Whitehead
    Pages 456-487

  12. Homotopy Operations

    • George W. Whitehead
    Pages 488-541

  13. Stable Homotopy and Homology

    • George W. Whitehead
    Pages 542-601

  14. Homology of Fibre Spaces

    • George W. Whitehead
    Pages 602-671

  15. Back Matter

    Pages 673-746
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Keywords

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.

Authors and Affiliations

  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

    George W. Whitehead

Bibliographic Information

  • Book Title: Elements of Homotopy Theory

  • Authors: George W. Whitehead

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-6318-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Science+Business Media, LLC, part of Springer Nature 1978

  • Hardcover ISBN: 978-0-387-90336-1Published: 19 January 1979

  • Softcover ISBN: 978-1-4612-6320-3Published: 02 April 2012

  • eBook ISBN: 978-1-4612-6318-0Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XXI, 746

  • Topics: Topology

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