Axiomatic Stable Homotopy Theory Paperback - 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 Axiomatic Stable Homotopy Theory Paperback write by Mark Hovey. This book was released on 2014-09-11. Axiomatic Stable Homotopy Theory Paperback available in PDF, EPUB and Kindle. This work gives an axiomatic presentation of stable homotopy theory. It starts with axioms defining a stable homotopy category; using these axioms, one can make various constructions - cellular towers, Bousfield localization, and Brown representability, to name a few. Much of the book is devoted to these constructions and to the study of the global structure of stable homotopy categories.
Axiomatic Stable Homotopy Theory
Axiomatic 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 Axiomatic Stable Homotopy Theory write by Mark Hovey. This book was released on 1997. Axiomatic Stable Homotopy Theory available in PDF, EPUB and Kindle. We define and investigate a class of categories with formal properties similar to those of the homotopy category of spectra. This class includes suitable versions of the derived category of modules over a commutative ring, or of comodules over a commutative Hopf algebra, and is closed under Bousfield localization. We study various notions of smallness, questions about representability of (co)homology functors, and various kinds of localization. We prove theorems analogous to those of Hopkins and Smith about detection of nilpotence and classification of thick subcategories. We define the class of Noetherian stable homotopy categories, and investigate their special properties. Finally, we prove that a number of categories occurring in nature (including those mentioned above) satisfy our axioms.
Axiomatic, Enriched and Motivic Homotopy Theory
Axiomatic, Enriched and Motivic 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 Axiomatic, Enriched and Motivic Homotopy Theory write by John Greenlees. This book was released on 2012-12-06. Axiomatic, Enriched and Motivic Homotopy Theory available in PDF, EPUB and Kindle. The NATO Advanced Study Institute "Axiomatic, enriched and rna tivic homotopy theory" took place at the Isaac Newton Institute of Mathematical Sciences, Cambridge, England during 9-20 September 2002. The Directors were J.P.C.Greenlees and I.Zhukov; the other or ganizers were P.G.Goerss, F.Morel, J.F.Jardine and V.P.Snaith. The title describes the content well, and both the event and the contents of the present volume reflect recent remarkable successes in model categor ies, structured ring spectra and homotopy theory of algebraic geometry. The ASI took the form of a series of 15 minicourses and a few extra lectures, and was designed to provide background, and to bring the par ticipants up to date with developments. The present volume is based on a number of the lectures given during the workshop. The ASI was the opening workshop of the four month programme "New Contexts for Stable Homotopy Theory" which explored several themes in greater depth. I am grateful to the Isaac Newton Institute for providing such an ideal venue, the NATO Science Committee for their funding, and to all the speakers at the conference, whether or not they were able to contribute to the present volume. All contributions were refereed, and I thank the authors and referees for their efforts to fit in with the tight schedule. Finally, I would like to thank my coorganizers and all the staff at the Institute for making the ASI run so smoothly. J.P.C.GREENLEES.
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.
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.
