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Cohomology Operations and Applications in Homotopy Theory

2008-01-01 Mathematics
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Release : 2008-01-01
Genre : Mathematics
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Book Rating : 647/5 ( reviews)

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Book Synopsis Cohomology Operations and Applications in Homotopy Theory by : Robert E. Mosher

Download or read book Cohomology Operations and Applications in Homotopy Theory written by Robert E. Mosher. This book was released on 2008-01-01. Available in PDF, EPUB and Kindle. Book excerpt: Cohomology operations are at the center of a major area of activity in algebraic topology. This treatment explores the single most important variety of operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications, including several different techniques of homotopy theory useful for computation. 1968 edition.

Cohomology Operations and Applications in Homotopy Theory [by] Robert E. Mosher [and] Martin C. Tangora

1968 Homology theory
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Release : 1968
Genre : Homology theory
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Book Rating : /5 ( reviews)

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Book Synopsis Cohomology Operations and Applications in Homotopy Theory [by] Robert E. Mosher [and] Martin C. Tangora by : Robert E. Mosher

Download or read book Cohomology Operations and Applications in Homotopy Theory [by] Robert E. Mosher [and] Martin C. Tangora written by Robert E. Mosher. This book was released on 1968. Available in PDF, EPUB and Kindle. Book excerpt:

Secondary Cohomology Operations

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 984/5 ( reviews)

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Book Synopsis Secondary Cohomology Operations by : John R. Harper

Download or read book Secondary Cohomology Operations written by John R. Harper. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: 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 now 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 manyapplications 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 ofmore 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.

Introduction to Homotopy Theory

2008 Mathematics
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Release : 2008
Genre : Mathematics
Kind : eBook
Book Rating : 366/5 ( reviews)

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Book Synopsis Introduction to Homotopy Theory by : Paul Selick

Download or read book Introduction to Homotopy Theory written by Paul Selick. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: Offers a summary for students and non-specialists who are interested in learning the basics of algebraic topology. This book covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, and generalized homology and cohomology operations.

Stable Homotopy and Generalised Homology

1974 Mathematics
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Release : 1974
Genre : Mathematics
Kind : eBook
Book Rating : 240/5 ( reviews)

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Book Synopsis Stable Homotopy and Generalised Homology by : John Frank Adams

Download or read book Stable Homotopy and Generalised Homology written by John Frank Adams. This book was released on 1974. Available in PDF, EPUB and Kindle. Book excerpt: J. Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in 1967, 1970, and 1971, the well-written notes of which are published in this classic in algebraic topology. The three series focused on Novikov's work on operations in complex cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology. Adams's exposition of the first two topics played a vital role in setting the stage for modern work on periodicity phenomena in stable homotopy theory. His exposition on the third topic occupies the bulk of the book and gives his definitive treatment of the Adams spectral sequence along with many detailed examples and calculations in KU-theory that help give a feel for the subject.

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