Algebraic Methods in Unstable Homotopy Theory

Inbunden, Engelska, 2010

Del 12 i serien New Mathematical Monographs

2 179 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2010-02-18
Mått:162 x 234 x 35 mm
Vikt:940 g
Format:Inbunden
Språk:Engelska
Serie:New Mathematical Monographs
Antal sidor:574
Förlag:Cambridge University Press
ISBN:9780521760379

Utforska kategorier

Topologi inom Naturvetenskap och teknik

Mer om författaren

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

Recensioner i media

'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

Innehållsförteckning

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.