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9780486466644

Cohomology Operations and Applications in Homotopy Theory

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  • ISBN13:

    9780486466644

  • ISBN10:

    0486466647

  • Format: Paperback
  • Copyright: 2008-06-26
  • Publisher: Dover Publications
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Summary

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.

Table of Contents

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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