**Graduate Studies in Mathematics**

Volume: 49;
2002;
268 pp;
Hardcover

MSC: Primary 55;

Print ISBN: 978-0-8218-3198-4

Product Code: GSM/49

List Price: $78.00

AMS Member Price: $62.40

MAA member Price: $70.20

**Electronic ISBN: 978-1-4704-2098-7
Product Code: GSM/49.E**

List Price: $78.00

AMS Member Price: $62.40

MAA member Price: $70.20

# Secondary Cohomology Operations

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*John R. Harper*

Although the theory and applications of secondary cohomology operations
are an important part of an advanced graduate-level 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 Massey-Peterson 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 self-study or as a
textbook for an advanced course on the topic. It is available in both hardcover
and softcover editions.

#### Readership

Graduate students and research mathematicians interested in algebraic topology.

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## Secondary Cohomology Operations

- Cover Cover11 free
- Title i2 free
- Copyright ii3 free
- Contents v6 free
- Preface vii8 free
- Chapter 1. Review of Primary Operations 114 free
- Chapter 2. Segue to Secondary Operations 4154
- Chapter 3. Fundamental Constructions 4558
- Chapter 4. Secondary Cohomology Operations 8598
- Chapter 5. Calculations with Secondary Operations 129142
- Chapter 6. The Hopf Invariant 179192
- Chapter 7. The Cohomology Structure of Universal Examples 199212
- Bibliography 261274
- Index 267280
- Back Cover Back Cover1282