Stable Homotopy and Generalised Homology
384 pages

51/4 x 8

© 1974
J. Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in 1967, 1970, and 1971, the wellwritten 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 KUtheory that help give a feel for the subject.
Contents
Preface
Pt. I: S.P. Novikov's Work on Operations on Complex Cobordism
2: Cobordism groups
3: Homology
4: The ConnerFloyd Chern classes
5: The Novikov operations
6: The algebra of all operations
7: Scholium on Novikov's exposition
8: Complex manifolds
Pt. II: Quillen's Work on Formal Groups and Complex Cobordism
1: Formal groups
2: Examples from algebraic topology
3: Reformulation
4: Calculations in Ehomology and cohomology
5: Lazard's universal ring
6: More calculations in Ehomology
7: The structure of Lazard's universal ring L
8: Quillen's theorem
9: Corollaries
10: Various formulae in [pi][subscript *](MU)
11: MU[subscript *](MU)
12: Behaviour of the Bott map
13: K[subscript *](K)
14: The HattoriStong theorem
15: Quillen's idempotent cohomology operations
16: The BrownPeterson spectrum
17: KO[subscript *](KO)
Pt. III: Stable Homotopy and Generalised Homology
2: Spectra
3: Elementary properties of the category of CWspectra
4: Smash products
5: SpanierWhitehead duality
6: Homology and cohomology
7: The AtiyahHirzebruch spectral sequence
8: The inverse limit and its derived functors
9: Products
10: Duality in manifolds
11: Applications in Ktheory
12: The Steenrod algebra and its dual
13: A universal coefficient theorem
14: A category of fractions
15: The Adams spectral sequence
16: Applications to [pi][subscript *](bu[actual symbol not
reproducible]X): modules over K[x, y]
17: Structure of [pi][subscript *](bu[actual symbol not
reproducible]bu)~
Pt. I: S.P. Novikov's Work on Operations on Complex Cobordism
2: Cobordism groups
3: Homology
4: The ConnerFloyd Chern classes
5: The Novikov operations
6: The algebra of all operations
7: Scholium on Novikov's exposition
8: Complex manifolds
Pt. II: Quillen's Work on Formal Groups and Complex Cobordism
1: Formal groups
2: Examples from algebraic topology
3: Reformulation
4: Calculations in Ehomology and cohomology
5: Lazard's universal ring
6: More calculations in Ehomology
7: The structure of Lazard's universal ring L
8: Quillen's theorem
9: Corollaries
10: Various formulae in [pi][subscript *](MU)
11: MU[subscript *](MU)
12: Behaviour of the Bott map
13: K[subscript *](K)
14: The HattoriStong theorem
15: Quillen's idempotent cohomology operations
16: The BrownPeterson spectrum
17: KO[subscript *](KO)
Pt. III: Stable Homotopy and Generalised Homology
2: Spectra
3: Elementary properties of the category of CWspectra
4: Smash products
5: SpanierWhitehead duality
6: Homology and cohomology
7: The AtiyahHirzebruch spectral sequence
8: The inverse limit and its derived functors
9: Products
10: Duality in manifolds
11: Applications in Ktheory
12: The Steenrod algebra and its dual
13: A universal coefficient theorem
14: A category of fractions
15: The Adams spectral sequence
16: Applications to [pi][subscript *](bu[actual symbol not
reproducible]X): modules over K[x, y]
17: Structure of [pi][subscript *](bu[actual symbol not
reproducible]bu)~
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