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Stable Homotopy and Generalised Homology

1974 Mathematics
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Release : 1974
Genre : Mathematics
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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.

Stable Homotopy and Generalized Homology

1974 Homology theory
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Release : 1974
Genre : Homology theory
Kind : eBook
Book Rating : /5 ( reviews)

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

Download or read book Stable Homotopy and Generalized Homology written by John Frank Adams. This book was released on 1974. Available in PDF, EPUB and Kindle. Book excerpt:

Stable Homotopy and Generalized Homology

1972 Homology theory
Download Stable Homotopy and Generalized Homology PDF Online Free

Author :
Release : 1972
Genre : Homology theory
Kind : eBook
Book Rating : /5 ( reviews)

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

Download or read book Stable Homotopy and Generalized Homology written by John Frank Adams. This book was released on 1972. Available in PDF, EPUB and Kindle. Book excerpt:

Nilpotence and Periodicity in Stable Homotopy Theory

1992-11-08 Mathematics
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Release : 1992-11-08
Genre : Mathematics
Kind : eBook
Book Rating : 728/5 ( reviews)

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Book Synopsis Nilpotence and Periodicity in Stable Homotopy Theory by : Douglas C. Ravenel

Download or read book Nilpotence and Periodicity in Stable Homotopy Theory written by Douglas C. Ravenel. This book was released on 1992-11-08. Available in PDF, EPUB and Kindle. Book excerpt: Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.

Equivariant Homotopy and Cohomology Theory

1996 Mathematics
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Release : 1996
Genre : Mathematics
Kind : eBook
Book Rating : 190/5 ( reviews)

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Book Synopsis Equivariant Homotopy and Cohomology Theory by : J. Peter May

Download or read book Equivariant Homotopy and Cohomology Theory written by J. Peter May. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt: This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. It explains the main ideas behind some of the most striking recent advances in the subject. The works begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. The book then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. The basic machinery that is needed to make serious use of equivariant stable homotopy theory is presented next, along with discussions of the Segal conjecture and generalized Tate cohomology. Finally, the book gives an introduction to "brave new algebra", the study of point-set level algebraic structures on spectra and its equivariant applications. Emphasis is placed on equivariant complex cobordism, and related results on that topic are presented in detail.

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