Algebraic Methods in Unstable Homotopy Theory
Algebraic Methods in Unstable Homotopy Theory
$205.00
USDThe 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.
- Methods are introduced one-by-one in chapters that are largely self-contained
- Suitable as a course text and also a valuable reference for experts and graduate students wishing to enter the field
- Contains over 270 exercises
Reviews & endorsements
"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
Product details
March 2010Hardback
9780521760379
574 pages
234 × 162 × 35 mm
0.94kg
275 exercises
Available
Table of Contents
- Preface
- Introduction
- 1. Homotopy groups with coefficients
- 2. A general theory of localization
- 3. Fibre extensions of squares and the Peterson-Stein formula
- 4. Hilton-Hopf invariants and the EHP sequence
- 5. James-Hopf invariants and Toda-Hopf invariants
- 6. Samelson products
- 7. Bockstein spectral sequences
- 8. Lie algebras and universal enveloping algebras
- 9. Applications of graded Lie algebras
- 10. Differential homological algebra
- 11. Odd primary exponent theorems
- 12. Differential homological algebra of classifying spaces
- Bibliography
- Index.
