# Stable Homotopy and Generalised Homology

- Publisher: Chicago University Press
- Binding: Paperback
- ISBN-13: 9780226005249
- Price in FC: USD 38.00
- Pages: 384
- Year of Pub / Reprint Year: 1974

## Description

**About the Book:**

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.

**Contents:**

Preface

Pt. I: S.P. Novikov’s Work on Operations on Complex Cobordism

2: Cobordism groups

3: Homology

4: The Conner-Floyd 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 E-homology and cohomology

5: Lazard’s universal ring

6: More calculations in E-homology

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 Hattori-Stong theorem

15: Quillen’s idempotent cohomology operations

16: The Brown-Peterson spectrum

17: KO[subscript *](KO)

Pt. III: Stable Homotopy and Generalised Homology

2: Spectra

3: Elementary properties of the category of CW-spectra

4: Smash products

5: Spanier-Whitehead duality

6: Homology and cohomology

7: The Atiyah-Hirzebruch spectral sequence

8: The inverse limit and its derived functors

9: Products

10: Duality in manifolds

11: Applications in K-theory

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)~