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  • © 2013

Rational Homotopy Theory and Differential Forms

Birkhäuser
  • Second edition with fully updated content

  • Includes a readable introduction for non-specialists

  • Provides many elementary examples and exercises

Part of the book series: Progress in Mathematics (PM, volume 16)

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eBook USD 119.00
Price excludes VAT (USA)
  • ISBN: 978-1-4614-8468-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
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  • Tax calculation will be finalised during checkout
Softcover Book USD 159.99
Price excludes VAT (USA)
Hardcover Book USD 159.99
Price excludes VAT (USA)

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xi
  2. Introduction

    • Phillip Griffiths, John Morgan
    Pages 1-3
  3. Basic Concepts

    • Phillip Griffiths, John Morgan
    Pages 5-20
  4. CW Homology Theorem

    • Phillip Griffiths, John Morgan
    Pages 21-25
  5. The Whitehead Theorem and the Hurewicz Theorem

    • Phillip Griffiths, John Morgan
    Pages 27-40
  6. Spectral Sequence of a Fibration

    • Phillip Griffiths, John Morgan
    Pages 41-52
  7. Obstruction Theory

    • Phillip Griffiths, John Morgan
    Pages 53-61
  8. Eilenberg–MacLane Spaces, Cohomology, and Principal Fibrations

    • Phillip Griffiths, John Morgan
    Pages 63-67
  9. Postnikov Towers and Rational Homotopy Theory

    • Phillip Griffiths, John Morgan
    Pages 69-81
  10. deRham’s Theorem for Simplicial Complexes

    • Phillip Griffiths, John Morgan
    Pages 83-93
  11. Differential Graded Algebras

    • Phillip Griffiths, John Morgan
    Pages 95-102
  12. Homotopy Theory of DGAs

    • Phillip Griffiths, John Morgan
    Pages 103-111
  13. DGAs and Rational Homotopy Theory

    • Phillip Griffiths, John Morgan
    Pages 113-118
  14. The Fundamental Group

    • Phillip Griffiths, John Morgan
    Pages 119-126
  15. Examples and Computations

    • Phillip Griffiths, John Morgan
    Pages 127-140
  16. Functorality

    • Phillip Griffiths, John Morgan
    Pages 141-149
  17. The Hirsch Lemma

    • Phillip Griffiths, John Morgan
    Pages 151-163
  18. Quillen’s Work on Rational Homotopy Theory

    • Phillip Griffiths, John Morgan
    Pages 165-176
  19. A ∞ -Structures and C ∞ -Structures

    • Phillip Griffiths, John Morgan
    Pages 177-185
  20. Exercises

    • Phillip Griffiths, John Morgan
    Pages 187-221

About this book

“Rational homotopy theory is today one of the major trends in algebraic topology. Despite the great progress made in only a few years, a textbook properly devoted to this subject still was lacking until now… The appearance of the text in book form is highly welcome, since it will satisfy the need of many interested people. Moreover, it contains an approach and point of view that do not appear explicitly in the current literature.”

—Zentralblatt MATH (Review of First Edition)

 

“The monograph is intended as an introduction to the theory of minimal models. Anyone who wishes to learn about the theory will find this book a very helpful and enlightening one. There are plenty of examples, illustrations, diagrams and exercises. The material is developed with patience and clarity. Efforts are made to avoid generalities and technicalities that may distract the reader or obscure the main theme. The theory and its power are elegantly presented. This is an excellent monograph.”

—Bulletin of the American Mathematical Society (Review of First Edition)

 

This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham’s theorem on simplical complexes. In addition, Sullivan’s results on computing the rational homotopy type from forms is presented.

 

New to the Second Edition:

*Fully-revised appendices including an expanded discussion of the Hirsch lemma

*Presentation of a natural proof of a Serre spectral sequence result

*Updated content throughout the book, reflecting advances in the area of homotopy theory

 

With its modern approach and timely revisions, this second edition of Rational Homotopy Theory and Differential Forms will be a valuable resource for graduate students and researchers in algebraic topology, differential forms, and homotopy theory.

Keywords

  • Brouwer's theorem
  • algebraic topology
  • cohomology
  • differential forms
  • homotopy
  • obstruction theory
  • rational homotopy theory
  • the Serre spectral sequence

Reviews

From the book reviews:

“This book is a second, augmented version of one of the famous books on rational homotopy. … The topological intuition throughout the book, the recollections of the necessary elementary homotopy theory and the list of exercises make this book an excellent introduction to Sullivan’s theory. … this book is highly recommended to anyone who wants to understand Sullivan’s theory of rational homotopy theory.” (Daniel Tanré, Mathematical Reviews, February, 2015)

Authors and Affiliations

  • School of Mathematics, Princeton University Institute for Advanced Study, Princeton, USA

    Phillip Griffiths

  • Simons Center for Geometry and Physics, Stonybrook University, Stonybrook, USA

    John Morgan

Bibliographic Information

Buying options

eBook USD 119.00
Price excludes VAT (USA)
  • ISBN: 978-1-4614-8468-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 159.99
Price excludes VAT (USA)
Hardcover Book USD 159.99
Price excludes VAT (USA)