Algebraic Methods in Unstable Homotopy Theory

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Cambridge University Press, Feb 18, 2010 - Mathematics
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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.
 

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Contents

Homotopy groups with coefficients
11
A general theory of localization
35
Fibre extensions of squares and the PetersonStein formula
94
HiltonHopf invariants and the EHP sequence
107
JamesHopf invariants and TodaHopf invariants
135
Samelson products
158
Lie algebras and universal enveloping algebras
251
Applications of graded Lie algebras
283
Differential homological algebra
313
Odd primary exponent theorems
437
Differential homological algebra of classifying spaces
489
Bibliography
545
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About the author (2010)

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

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