CONTENTS

Page

Abstract ii

Introduction v

Chapter 1, Algebraic Information 1

Introduction 1

1.1 Recollections and Notations 1

1.2 A Theorem of Massey, Peterson and Barcus 5

1.3 Methods for Calculating Exts(M,N) 8

l.U Facts Concerning the Cohomology of the Steenrod Algebra 10

Chapter 2, Adams Resolutions and Obstruction Theory 14

Introduction 14

2.1 Realization Theory 15

2.2 Homological Criterion for Lifting Maps 24

2.3 Power Spaces 26

2.4 A Homological Criterion for H-Structures 35

Chapter 3, Proof of Theorem B 39

3.1 Outline of the Argument 39

3.2 Preliminary Calculations 39

3.3 A Certain 3-Stage Postnikov System 43

3.4 Conclusion of the Proof of Theorem B 48

Chapter 4, Theorem A and Applications 61

4.1 Theorem A and Examples . . 61

4.2 Torsion and Associativity 63

4.3 Quasi-Regularity of Finite H-Spaces 65

4.4 Mod p Decompositions of F^ and Eg 66

Appendix 69

References 71

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