Neisendorfer J.A. Algebraic Methods in Unstable Homotopy Theory

Cambridge University Press, UK, 2010. — 597 p. — (new mathematical monographs 12) — ISBN10: 0521760372The 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.Homotopy groups with coefficient
A general theory of localization
Fibre extensions of squares and the Peterson–Stein formula
Hilton–Hopf invariants and the EHP sequence
James–Hopf invariants and Toda–Hopf invariants
Samelson products
Bockstein spectral sequences
Lie algebras and universal enveloping algebras
Applications of graded Lie algebras
Differential homological algebra
Odd primary exponent theorems
Differential homological algebra of classifying spaces