Steenrod squares in spectral sequences

Cover......Page 1
Steenrod Squares in Spectral Sequences......Page 2
QA612.8.S56 2006 515'.24-dc22......Page 3
Contents......Page 4
Preface......Page 6
1. Vector Spaces......Page 14
2. Algebras, Coalgebras, and Modules......Page 17
4. Bialgebras and Hopf Algebras......Page 21
6. Algebras with Coproducts......Page 28
7. Chains and Cochains......Page 33
8. Differential Algebras and Coalgebras......Page 36
9. Simplicial 8-Modules......Page 38
10. Homology of Simplicial Sets and Simplicial Groups......Page 42
11. Cotriples, Simplicial Objects, and Projective Resolutions......Page 48
12. Simplicial Theta-Coalgebras and Steenrod Operations......Page 50
13. Steenrod Operations on the Cohomology of Simplicial Sets......Page 53
14. Steenrod Operations on the Cohomology of Hopf Algebras......Page 54
15. Bisimplicial Objects......Page 57
16. The Spectral Sequence of a Bisimplicial Theta-Module......Page 58
17. Cup-k Products and Bisimplicial Theta-Modules......Page 60
CHAPTER 2  The Spectral Sequence of a Bisimplicial Coalgebra......Page 62
1. Bisimplicial Theta-Coalgebras......Page 63
2. Filtrations......Page 66
3. The Spectral Sequence......Page 68
4. Bisimplicial Sets with Group Action......Page 78
5. Application to the Serre Spectral Sequence......Page 84
6. Application to Andre-Quillen Cohomology......Page 86
1. Left Action by a Bialgebra......Page 88
2. Left Action by an Algebra with Coproducts......Page 97
3. Right Action by a Hopf algebra......Page 102
CHAPTER 4  Extensions of Hopf Algebras......Page 108
1. Convolutions and Conjugations......Page 109
2. Some Properties of Extensions......Page 115
3. Adjunction Isomorphism and Change-of-Rings Spectral Se......Page 120
1. The Spectral Sequence with its Products and Steenrod Squares......Page 126
2. Steenrod Operations on Ext€......Page 128
4. The Operations at the E2-level......Page 133
6. A Simple E"ample......Page 137
6. Application to the Cohomology of the Steenrod Algebra......Page 139
7. Application to Finite sub-Hopf Algebras of the Steenrod Algebra......Page 140
8. Applications to the Cohomology of Groups......Page 142
CHAPTER 6  The Eilenberg-Moore Spectral Sequence......Page 144
1. Kan Fibrations and Twisted Cartesian Products......Page 145
2. Bisimplicial Models for Fiber Bundles......Page 146
3. Construction of the Spectral Sequence......Page 150
1. The Spectral Sequence with its Products and Steenrod Squares......Page 154
2. Steenrod Operations on Ext......Page 155
3. The Operations at the E2-level......Page 157
4. Applications......Page 161
Bibliography......Page 162
Index......Page 166