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Hardcover ISBN:  9780821841419 
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Hardcover ISBN:  9780821841419 
Product Code:  SURV/129 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470413569 
Product Code:  SURV/129.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821841419 
eBook ISBN:  9781470413569 
Product Code:  SURV/129.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 129; 2006; 155 ppMSC: Primary 16; 18; 55;
This book develops a general theory of Steenrod operations in spectral sequences. It gives special attention to the changeofrings spectral sequence for the cohomology of an extension of Hopf algebras and to the Eilenberg–Moore spectral sequence for the cohomology of classifying spaces and homotopy orbit spaces. In treating the changeofrings spectral sequence, the book develops from scratch the necessary properties of extensions of Hopf algebras and constructs the spectral sequence in a form particularly suited to the introduction of Steenrod squares. The resulting theory can be used effectively for the computation of the cohomology rings of groups and Hopf algebras, and of the Steenrod algebra in particular, and so should play a useful role in stable homotopy theory. Similarly the book offers a selfcontained construction of the Eilenberg–Moore spectral sequence, in a form suitable for the introduction of Steenrod operations. The corresponding theory is an effective tool for the computation of the cohomology rings of the classifying spaces of the exceptional Lie groups, and it promises to be equally useful for the computation of the cohomology rings of homotopy orbit spaces and of the classifying spaces of loop groups.
ReadershipGraduate students and research mathematicians interested in algebraic topology.

Table of Contents

Chapters

1. Conventions

2. The spectral sequence of a bisimplicial coalgebra

3. Bialgebra actions on the cohomology of algebras

4. Extensions of Hopf algebras

5. Steenrod operations in the changeofrings spectral sequence

6. The EilenbergMoore spectral sequence

7. Steenrod Operations in the EilenbergMoore spectral sequence


Additional Material

Reviews

...this book gives a definitive reference on Steenrod operations in first quadrant spectral sequences addressed to experts or experienced mathematicians interested in applications of the theory.
Zentralblatt MATH


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This book develops a general theory of Steenrod operations in spectral sequences. It gives special attention to the changeofrings spectral sequence for the cohomology of an extension of Hopf algebras and to the Eilenberg–Moore spectral sequence for the cohomology of classifying spaces and homotopy orbit spaces. In treating the changeofrings spectral sequence, the book develops from scratch the necessary properties of extensions of Hopf algebras and constructs the spectral sequence in a form particularly suited to the introduction of Steenrod squares. The resulting theory can be used effectively for the computation of the cohomology rings of groups and Hopf algebras, and of the Steenrod algebra in particular, and so should play a useful role in stable homotopy theory. Similarly the book offers a selfcontained construction of the Eilenberg–Moore spectral sequence, in a form suitable for the introduction of Steenrod operations. The corresponding theory is an effective tool for the computation of the cohomology rings of the classifying spaces of the exceptional Lie groups, and it promises to be equally useful for the computation of the cohomology rings of homotopy orbit spaces and of the classifying spaces of loop groups.
Graduate students and research mathematicians interested in algebraic topology.

Chapters

1. Conventions

2. The spectral sequence of a bisimplicial coalgebra

3. Bialgebra actions on the cohomology of algebras

4. Extensions of Hopf algebras

5. Steenrod operations in the changeofrings spectral sequence

6. The EilenbergMoore spectral sequence

7. Steenrod Operations in the EilenbergMoore spectral sequence

...this book gives a definitive reference on Steenrod operations in first quadrant spectral sequences addressed to experts or experienced mathematicians interested in applications of the theory.
Zentralblatt MATH