Secondary cohomology operations / John R. Harper.

Format:

Book

Author/Creator:

Harper, John R., 1941- author.

Series:

Graduate studies in mathematics ; v. 49.

Graduate studies in mathematics, 1065-7339 ; volume 49

Language:

English

Subjects (All):

Homology theory.

Physical Description:

1 online resource (280 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2002]

Language Note:

English

Summary:

The book develops the theory of secondary cohomology operations for singular cohomology theory. The author develops the subject 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 written for 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.

Contents:

""Cover""; ""Title""; ""Copyright""; ""Contents""; ""Preface""; ""Chapter 1. Review of Primary Operations""; ""Â1.1. Primary cohomology operations""; ""Â1.2. Steenrod operations and the Steenrod algebra""; ""Â1.3. Cohomology operations and Eilenberg-Mac Lane spaces""; ""Â1.4. Steenrod operations and maps between spheres""; ""Â1.5. Steenrod operations for odd primes""; ""Chapter 2. Segue to Secondary Operations""; ""Chapter 3. Fundamental Constructions""; ""Â3.1. Terminology and conventions""; ""Â3.2. Basic constructions""; ""Â3.3. Dependence on homotopies""

""Â3.4. Peterson-Stein formulas""""Â3.5. The Milnor filtration""; ""Chapter 4. Secondary Cohomology Operations""; ""Â4.1. Definitions""; ""Â4.2. The fundamental theorem for secondary operations""; ""Â4.3. Higher order operations""; ""Chapter 5. Calculations with Secondary Operations""; ""Â5.1. Operations based on Sq(2)Sq(n)""; ""Â5.2. Higher order Bocksteins""; ""Â5.3. The Adams operations""; ""Â5.4. The Liulevicius-Shimada-Yamanoshita operations""; ""Â5.5. Operations based on unstable relations""; ""Chapter 6. The Hopf Invariant""; ""Â6.1. The classical Hopf invariant""

""Â6.2. Hopf invariant one""""Chapter 7. The Cohomology Structure of Universal Examples""; ""Â7.1. Unstable modules and algebras over the Steenrod algebra""; ""Â7.2. Massey-Peterson""; ""Â7.3. Products""; ""Bibliography""; ""Index ""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""H""; ""I""; ""K""; ""L""; ""M""; ""N""; ""P""; ""S""; ""T""; ""Z""; ""Back Cover""

Notes:

Description based upon print version of record.

Includes bibliographical references (pages 261-266) and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

1-4704-2098-8

OCLC:

922965113