J. Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in 1967, 1970, and 1971, the well-written notes of which are published in this classic in algebraic topology. The three series focused on Novikov's work on operations in complex cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology. Adams's exposition of the first two topics played a vital role in setting the stage for modern work on periodicity phenomena in stable homotopy theory. His exposition on the third topic occupies the bulk of the book and gives his definitive treatment of the Adams spectral sequence along with many detailed examples and calculations in KU-theory that help give a feel for the subject.
Author(s): John Frank Adams
Edition: LaTeX
Publisher: University of Chicago Press
Year: 2022
Language: English
Pages: 397
I S.P. Novikov's Work on Operations on Complex Cobordism
Introduction
Cobordism Groups
Homology
The Conner-Floyd Chern Classes
The Novikov Operations
The algebra of all operations
Scholium on Novikov's Exposition
Complex Manifolds
II Quillen's Work on Formal Groups and Complex Cobordism
Introduction
Formal Groups
Examples from Algebraic Topology
Reformulation
Calculations in E-Homology and Cohomology
Lazard's Universal Ring
More calculations in E-Homology
The Structure of Lazard's Universal Ring L
Quillen's Theorem
Corollaries
Various Formulae in (MU)
MU(MU)
Behaviour of the Bott map
K(K)
The Hattori-Stong theorem
Quillen's Idempotent Cohomology Operations
The Brown-Peterson spectrum
KO(KO) (Added May 1970)
III Stable Homotopy and Generalized Homology
Introduction
Spectra
Elementary properties of the category of CW-spectra
Smash products
Spanier-Whitehead Duality
Homology and Cohomology
The Atiyah-Hirzebruch Spectral Sequence
The Inverse Limit and its Derived Functors
Products
Duality in Manifolds
Applications in K-Theory
The Steenrod Algebra and its Dual
A Universal Coefficient Theorem
A Category of Fractions
The Adams spectral sequence
Applications to (bu X); Modules over K[x, y]
Structure of *(bubu)
