Secondary cohomology operations / John R. Harper.

Format:

Book

Author/Creator:

Harper, John R., 1941-

Series:

Graduate studies in mathematics 1065-7339 ; v. 49.

Graduate studies in mathematics, 1065-7339 ; v. 49

Language:

English

Subjects (All):

Homology theory.

Physical Description:

xi, 268 pages : illustrations ; 26 cm.

Place of Publication:

Providence, R.I. : American Mathematical Society, [2002]

Contents:

Chapter 1. Review of Primary Operations 1

1.1. Primary cohomology operations 1

1.2. Steenrod operations and the Steenrod algebra 4

1.3. Cohomology operations and Eilenberg-Mac Lane spaces 21

1.4. Steenrod operations and maps between spheres 29

1.5. Steenrod operations for odd primes 33

Chapter 2. Segue to Secondary Operations 41

Chapter 3. Fundamental Constructions 45

3.1. Terminology and conventions 45

3.2. Basic constructions 49

3.3. Dependence on homotopies 60

3.4. Peterson-Stein formulas 64

3.5. The Milnor filtration 69

Chapter 4. Secondary Cohomology Operations 85

4.2. The fundamental theorem for secondary operations 90

4.3. Higher order operations 121

Chapter 5. Calculations with Secondary Operations 129

5.1. Operations based on Sq(2)Sq(n) 129

5.2. Higher order Bocksteins 138

5.3. The Adams operations 147

5.4. The Liulevicius-Shimada-Yamanoshita operations 155

5.5. Operations based on unstable relations 160

Chapter 6. The Hopf Invariant 179

6.1. The classical Hopf invariant 179

6.2. Hopf invariant one 188

Chapter 7. The Cohomology Structure of Universal Examples 199

7.1. Unstable modules and algebras over the Steenrod algebra 199

7.2. Massey-Peterson fibrations 205

7.3. Products 229.

Notes:

Includes bibliographical references (pages 261-266) and index.

ISBN:

0821831984

0821832700

OCLC:

49519159