Foundations of Stable Homotopy Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Foundations of Stable Homotopy Theory write by David Barnes. This book was released on 2020-03-26. Foundations of Stable Homotopy Theory available in PDF, EPUB and Kindle. The beginning graduate student in homotopy theory is confronted with a vast literature on spectra that is scattered across books, articles and decades. There is much folklore but very few easy entry points. This comprehensive introduction to stable homotopy theory changes that. It presents the foundations of the subject together in one place for the first time, from the motivating phenomena to the modern theory, at a level suitable for those with only a first course in algebraic topology. Starting from stable homotopy groups and (co)homology theories, the authors study the most important categories of spectra and the stable homotopy category, before moving on to computational aspects and more advanced topics such as monoidal structures, localisations and chromatic homotopy theory. The appendix containing essential facts on model categories, the numerous examples and the suggestions for further reading make this a friendly introduction to an often daunting subject.
Stable Homotopy and Generalised Homology
Stable Homotopy and Generalised Homology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stable Homotopy and Generalised Homology write by John Frank Adams. This book was released on 1974. Stable Homotopy and Generalised Homology available in PDF, EPUB and Kindle. 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.
Nilpotence and Periodicity in Stable Homotopy Theory
Nilpotence and Periodicity in Stable Homotopy Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nilpotence and Periodicity in Stable Homotopy Theory write by Douglas C. Ravenel. This book was released on 1992-11-08. Nilpotence and Periodicity in Stable Homotopy Theory available in PDF, EPUB and Kindle. 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 Stable Homotopy Theory
Equivariant Stable Homotopy Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Equivariant Stable Homotopy Theory write by L. Gaunce Jr. Lewis. This book was released on 2006-11-14. Equivariant Stable Homotopy Theory available in PDF, EPUB and Kindle. This book is a foundational piece of work in stable homotopy theory and in the theory of transformation groups. It may be roughly divided into two parts. The first part deals with foundations of (equivariant) stable homotopy theory. A workable category of CW-spectra is developed. The foundations are such that an action of a compact Lie group is considered throughout, and spectra allow desuspension by arbitrary representations. But even if the reader forgets about group actions, he will find many details of the theory worked out for the first time. More subtle constructions like smash products, function spectra, change of group isomorphisms, fixed point and orbit spectra are treated. While it is impossible to survey properly the material which is covered in the book, it does boast these general features: (i) a thorough and reliable presentation of the foundations of the theory; (ii) a large number of basic results, principal applications, and fundamental techniques presented for the first time in a coherent theory, unifying numerous treatments of special cases in the literature.
Modern Classical Homotopy Theory
Modern Classical Homotopy Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Modern Classical Homotopy Theory write by Jeffrey Strom. This book was released on 2023-01-19. Modern Classical Homotopy Theory available in PDF, EPUB and Kindle. The core of classical homotopy theory is a body of ideas and theorems that emerged in the 1950s and was later largely codified in the notion of a model category. This core includes the notions of fibration and cofibration; CW complexes; long fiber and cofiber sequences; loop spaces and suspensions; and so on. Brown's representability theorems show that homology and cohomology are also contained in classical homotopy theory. This text develops classical homotopy theory from a modern point of view, meaning that the exposition is informed by the theory of model categories and that homotopy limits and colimits play central roles. The exposition is guided by the principle that it is generally preferable to prove topological results using topology (rather than algebra). The language and basic theory of homotopy limits and colimits make it possible to penetrate deep into the subject with just the rudiments of algebra. The text does reach advanced territory, including the Steenrod algebra, Bott periodicity, localization, the Exponent Theorem of Cohen, Moore, and Neisendorfer, and Miller's Theorem on the Sullivan Conjecture. Thus the reader is given the tools needed to understand and participate in research at (part of) the current frontier of homotopy theory. Proofs are not provided outright. Rather, they are presented in the form of directed problem sets. To the expert, these read as terse proofs; to novices they are challenges that draw them in and help them to thoroughly understand the arguments.
