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Secondary Cohomology Operations
John R. Harper, University of Rochester, NY

Also Available in Hardcover GSM/49


Graduate Studies in Mathematics
2002; 268 pp; softcover
Volume: 49
ISBN-10: 0-8218-3270-0
ISBN-13: 978-0-8218-3270-7
List Price: US$60
Member Price: US$48
Order Code: GSM/49.S
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Secondary Cohomology Operations - 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.


Graduate students and research mathematicians interested in algebraic topology.


"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

Table of Contents

  • Review of primary operations
  • Segue to secondary operations
  • Fundamental constructions
  • Secondary cohomology operations
  • Calculations with secondary operations
  • The Hopf invariant
  • The cohomology structure of universal examples
  • Bibliography
  • Index
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