Algebraic Methods in Unstable Homotopy Theory

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

• 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.

'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 expects in the area.' Bulletin of the London Mathematical Society