Algebraic Methods in Unstable Homotopy Theory (New Mathematical Monographs, Series Number 12)

"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"--Provided by publisher. "This is a comprehensive up-to-date treatment of unstable homotopy. 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. In largely self-contained chapters 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"--Provided by publisher. Machine generated contents note: 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. The focus of this work is on those methods from algebraic topology which underlie the work of Cohen, Moore, and the author. Suitable for a course in unstable homotopy theory, it is also a valuable reference for experts and graduate students alike