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Steenrod Squares in Spectral Sequences
 
William M. Singer Fordham University, Bronx, NY
Steenrod Squares in Spectral Sequences
Hardcover ISBN:  978-0-8218-4141-9
Product Code:  SURV/129
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1356-9
Product Code:  SURV/129.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-4141-9
eBook: ISBN:  978-1-4704-1356-9
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
Steenrod Squares in Spectral Sequences
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Steenrod Squares in Spectral Sequences
William M. Singer Fordham University, Bronx, NY
Hardcover ISBN:  978-0-8218-4141-9
Product Code:  SURV/129
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1356-9
Product Code:  SURV/129.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-4141-9
eBook ISBN:  978-1-4704-1356-9
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 Details
     
     
    Mathematical Surveys and Monographs
    Volume: 1292006; 155 pp
    MSC: Primary 16; 18; 55;

    This book develops a general theory of Steenrod operations in spectral sequences. It gives special attention to the change-of-rings 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 change-of-rings 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 self-contained 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.

    Readership

    Graduate 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 change-of-rings spectral sequence
    • 6. The Eilenberg-Moore spectral sequence
    • 7. Steenrod Operations in the Eilenberg-Moore spectral sequence
  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1292006; 155 pp
MSC: Primary 16; 18; 55;

This book develops a general theory of Steenrod operations in spectral sequences. It gives special attention to the change-of-rings 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 change-of-rings 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 self-contained 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.

Readership

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 change-of-rings spectral sequence
  • 6. The Eilenberg-Moore spectral sequence
  • 7. Steenrod Operations in the Eilenberg-Moore 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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