This treatment explores the single most important variety of cohomology operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications. 1968 edition.
This treatment explores the single most important variety of cohomology operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications. 1968 edition.
Preface 1. Introduction to cohomology operations 2. Construction of the Steenrod squares 3. Properties of the squares 4. Application: the Hopf invariant 5. Application: vector fields on spheres 6. The Steenrod algebra 7. Exact couples and spectral sequences 8. Fibre spaces 9. Cohomology of K(pi, n) 10. Classes of Abelian groups 11. More about fiber spaces 12. Applications: some homotopy groups of spheres 13. n-Type and Postnikov systems 14. Mapping sequences and homotopy classification 15. Properties of the stable range 16. Higher cohomology operations 17. Compositions in the stable homotopy of spheres 18. The Adams spectral sequence Bibliography Index
Preface 1. Introduction to cohomology operations 2. Construction of the Steenrod squares 3. Properties of the squares 4. Application: the Hopf invariant 5. Application: vector fields on spheres 6. The Steenrod algebra 7. Exact couples and spectral sequences 8. Fibre spaces 9. Cohomology of K(pi, n) 10. Classes of Abelian groups 11. More about fiber spaces 12. Applications: some homotopy groups of spheres 13. n-Type and Postnikov systems 14. Mapping sequences and homotopy classification 15. Properties of the stable range 16. Higher cohomology operations 17. Compositions in the stable homotopy of spheres 18. The Adams spectral sequence Bibliography Index
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