Algebraic methods in unstable homotopy theory / Joseph Neisendorfer.

Format:

Book

Author/Creator:

Neisendorfer, Joseph, 1945- author.

Series:

New mathematical monographs ; 12.

New mathematical monographs ; 12

Language:

English

Subjects (All):

Homotopy theory.

Algebraic topology.

Physical Description:

1 online resource (xix, 554 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2010.

Language Note:

English

Summary:

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.

Contents:

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.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 545-549) and index.

ISBN:

1-107-20781-9

1-282-81789-2

9786612817892

0-511-68947-0

0-511-68872-5

0-511-69095-9

0-511-69207-2

0-511-69021-5

0-511-69163-7

OCLC:

670410999