Cohomology Operations and Applications in Homotopy Theory

Cohomology operations are at the center of a major area of activity in algebraic topology. This treatment explores the single most important variety of operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications, including several different techniques of homotopy theory useful for computation.

Preface1. Introduction to cohomology operations2. Construction of the Steenrod squares3. Properties of the squares4. Application: the Hopf invariant5. Application: vector fields on spheres6. The Steenrod algebra7. Exact couples and spectral sequences8. Fibre spaces9. Cohomology of K(pi, n)10. Classes of Abelian groups11. More about fiber spaces12. Applications: some homotopy groups of spheres13. n-Type and Postnikov systems14. Mapping sequences and homotopy classification15. Properties of the stable range16. Higher cohomology operations17. Compositions in the stable homotopy of spheres18. The Adams spectral sequenceBibliographyIndex