Algebraic Methods in Unstable Homotopy Theory

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The most modern and thorough treatment of unstable homotopy theory available. The focus is on those methods from algebraic topology which are needed in the presentation of results, proven by Cohen, Moore, and the author, on the exponents of homotopy groups. The author introduces various aspects of unstable homotopy theory, including: homotopy groups with coefficients; localization and completion; the Hopf invariants of Hilton, James, and Toda; Samelson products; homotopy Bockstein spectral sequences; graded Lie algebras; differential homological algebra; and the exponent theorems concerning the homotopy groups of spheres and Moore spaces. This book is suitable for a course in unstable homotopy theory, following a first course in homotopy theory. It is also a valuable reference for both experts and graduate students wishing to enter the field.

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Editorial Reviews

From the Publisher
"It is very well written and organized, as would be expected of the author, who is renowned for an excellent expository style. The book could, and should, be used as a text for students aiming to do research in unstable homotopy theory. By the end of a thorough reading, a student would be well grounded in a suite of contemporary methods and would be ready to tackle research problems. The book's comprehensive nature also means that it is a wonderful reference for experts in the area. In conclusion, this is a very good book and anyone in the field ought to have it near to hand."
Stephen Theriault, Bulletin of the London Mathematical Society

"... provides a new generation of topologists with a readable and workmanlike collection of important techniques and results, arranged in a readable sequence, with many interesting applications (not available anywhere else in a single source) treated in a unified manner."
David A. Blanc, Mathematical Reviews

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Product Details

  • ISBN-13: 9780521760379
  • Publisher: Cambridge University Press
  • Publication date: 3/31/2010
  • Series: New Mathematical Monographs Series , #12
  • Pages: 574
  • Product dimensions: 6.20 (w) x 9.00 (h) x 1.60 (d)

Meet the Author

Joseph Neisendorfer is Professor Emeritus in the Department of Mathematics at the University of Rochester, New York.

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Table of Contents

Introduction to unstable homotopy theory 1

1 Homotopy groups with coefficients 11

2 A general theory of localization 35

3 Fibre extensions of squares and the Peterson-Stein formula 94

4 Hilton-Hopf invariants and the EHP sequence 107

5 James-Hopf invariants and Toda-Hopf invariants 135

6 Samelson products 158

7 Bockstein spectral sequences 221

8 Lie algebras and universal enveloping algebras 251

9 Applications of graded Lie algebras 283

10 Differential homological algebra 313

11 Odd primary exponent theorems 437

12 Differential homological algebra of classifying spaces 489

Bibliography 545

Index 550

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