Algebraic Methods in Unstable Homotopy Theory

The most modern and thorough treatment of unstable homotopy theory available.

Joseph Neisendorfer (Author)

9780521760379, Cambridge University Press

Hardback, published 18 February 2010

574 pages, 275 exercises
23.4 x 16.2 x 3.5 cm, 0.94 kg

'… provides a new generation of topologists with a readable and workmanlike collection of important techniques and results …' Mathematical Reviews

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.

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.

Subject Areas: Algebraic topology [PBPD]