Also Available in Softcover GSM/49.S
Hardcover ISBN:  9780821831984 
Product Code:  GSM/49 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470420987 
Product Code:  GSM/49.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821831984 
eBook: ISBN:  9781470420987 
Product Code:  GSM/49.B 
List Price:  $220.00 $177.50 
MAA Member Price:  $198.00 $159.75 
AMS Member Price:  $176.00 $142.00 
Also Available in Softcover GSM/49.S
Hardcover ISBN:  9780821831984 
Product Code:  GSM/49 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470420987 
Product Code:  GSM/49.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821831984 
eBook ISBN:  9781470420987 
Product Code:  GSM/49.B 
List Price:  $220.00 $177.50 
MAA Member Price:  $198.00 $159.75 
AMS Member Price:  $176.00 $142.00 

Book DetailsGraduate Studies in MathematicsVolume: 49; 2002; 268 ppMSC: Primary 55
Although the theory and applications of secondary cohomology operations are an important part of an advanced graduatelevel algebraic topology course, there are few books on the subject. The AMS fills that gap with the publication of the present volume.
The author's main purpose in this book is to develop the theory of secondary cohomology operations for singular cohomology theory, which is treated in terms of elementary constructions from general homotopy theory. Among many applications considered are the Hopf invariant one theorem (for all primes \(p\), including \(p = 2\)), Browder's theorem on higher Bockstein operations, and cohomology theory of MasseyPeterson fibrations.
Numerous examples and exercises help readers to gain a working knowledge of the theory. A summary of more advanced parts of the core material is included in the first chapter. Prerequisite is basic algebraic topology, including the Steenrod operations.
The book is geared toward graduate students and research mathematicians interested in algebraic topology and can be used for selfstudy or as a textbook for an advanced course on the topic. It is available in both hardcover and softcover editions.
ReadershipGraduate students and research mathematicians interested in algebraic topology.

Table of Contents

Chapters

Chapter 1. Review of primary operations

Chapter 2. Segue to secondary operations

Chapter 3. Fundamental constructions

Chapter 4. Secondary cohomology operations

Chapter 5. Calculations with secondary operations

Chapter 6. The Hopf invariant

Chapter 7. The cohomology structure of universal examples


Reviews

The book contains many examples and exercises and new material not published elsewhere. This book can be warmly recommended to readers interested in homotopy theory.
Zentralblatt MATH 
In all, this book gives an excellent introduction ... to a technical, but extremely important field ... This book is highly recommended for both beginners and experts.
Mathematical Reviews


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 Book Details
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Although the theory and applications of secondary cohomology operations are an important part of an advanced graduatelevel algebraic topology course, there are few books on the subject. The AMS fills that gap with the publication of the present volume.
The author's main purpose in this book is to develop the theory of secondary cohomology operations for singular cohomology theory, which is treated in terms of elementary constructions from general homotopy theory. Among many applications considered are the Hopf invariant one theorem (for all primes \(p\), including \(p = 2\)), Browder's theorem on higher Bockstein operations, and cohomology theory of MasseyPeterson fibrations.
Numerous examples and exercises help readers to gain a working knowledge of the theory. A summary of more advanced parts of the core material is included in the first chapter. Prerequisite is basic algebraic topology, including the Steenrod operations.
The book is geared toward graduate students and research mathematicians interested in algebraic topology and can be used for selfstudy or as a textbook for an advanced course on the topic. It is available in both hardcover and softcover editions.
Graduate students and research mathematicians interested in algebraic topology.

Chapters

Chapter 1. Review of primary operations

Chapter 2. Segue to secondary operations

Chapter 3. Fundamental constructions

Chapter 4. Secondary cohomology operations

Chapter 5. Calculations with secondary operations

Chapter 6. The Hopf invariant

Chapter 7. The cohomology structure of universal examples

The book contains many examples and exercises and new material not published elsewhere. This book can be warmly recommended to readers interested in homotopy theory.
Zentralblatt MATH 
In all, this book gives an excellent introduction ... to a technical, but extremely important field ... This book is highly recommended for both beginners and experts.
Mathematical Reviews