Algebraic Methods in Unstable Homotopy Theory

Algebraic Methods in Unstable Homotopy Theory

by Joseph Neisendorfer
     
 

ISBN-10: 0521760372

ISBN-13: 9780521760379

Pub. Date: 03/31/2010

Publisher: Cambridge University Press

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

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Overview

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.

Product Details

ISBN-13:
9780521760379
Publisher:
Cambridge University Press
Publication date:
03/31/2010
Series:
New Mathematical Monographs Series, #12
Pages:
574
Product dimensions:
6.20(w) x 9.00(h) x 1.60(d)

Related Subjects

Table of Contents

Introduction to unstable homotopy theory 1

1 Homotopy groups with coefficients 11

2 A general theory of localization 35

3 Fibre extensions of squares and the Peterson-Stein formula 94

4 Hilton-Hopf invariants and the EHP sequence 107

5 James-Hopf invariants and Toda-Hopf invariants 135

6 Samelson products 158

7 Bockstein spectral sequences 221

8 Lie algebras and universal enveloping algebras 251

9 Applications of graded Lie algebras 283

10 Differential homological algebra 313

11 Odd primary exponent theorems 437

12 Differential homological algebra of classifying spaces 489

Bibliography 545

Index 550

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