Algebraic methods in unstable homotopy theory /
Neisendorfer, Joseph, 1945-
Algebraic methods in unstable homotopy theory / Joseph Neisendorfer. - Cambridge : Cambridge University Press, 2010. - 1 online resource (xix, 554 pages) : digital, PDF file(s). - New mathematical monographs ; 12 . - New mathematical monographs ; 12. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Homotopy groups with coefficients -- 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. 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 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.
9780511691638 (ebook)
Homotopy theory.
Algebraic topology.
QA612.7 / .N45 2010
514/.24
Algebraic methods in unstable homotopy theory / Joseph Neisendorfer. - Cambridge : Cambridge University Press, 2010. - 1 online resource (xix, 554 pages) : digital, PDF file(s). - New mathematical monographs ; 12 . - New mathematical monographs ; 12. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Homotopy groups with coefficients -- 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. 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 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.
9780511691638 (ebook)
Homotopy theory.
Algebraic topology.
QA612.7 / .N45 2010
514/.24