Nilpotence and Periodicity in Stable Homotopy Theory. (AM-128), Volume 128 - 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. (AM-128), Volume 128 write by Douglas C. Ravenel. This book was released on 2016-03-02. Nilpotence and Periodicity in Stable Homotopy Theory. (AM-128), Volume 128 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 It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.
The Local Structure of Algebraic K-Theory
The Local Structure of Algebraic K-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 The Local Structure of Algebraic K-Theory write by Bjørn Ian Dundas. This book was released on 2012-09-06. The Local Structure of Algebraic K-Theory available in PDF, EPUB and Kindle. Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology.
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. Nilpotence and periodicity in Stable Homotopy Theory available in PDF, EPUB and Kindle.
Surveys on surgery theory : papers dedicated to C.T.C. Wall.
Surveys on surgery theory : papers dedicated to C.T.C. Wall. - 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 Surveys on surgery theory : papers dedicated to C.T.C. Wall. write by Sylvain Cappell. This book was released on 2000. Surveys on surgery theory : papers dedicated to C.T.C. Wall. available in PDF, EPUB and Kindle.
Bousfield Classes and Ohkawa's Theorem
Bousfield Classes and Ohkawa's Theorem - 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 Bousfield Classes and Ohkawa's Theorem write by Takeo Ohsawa. This book was released on 2020-03-18. Bousfield Classes and Ohkawa's Theorem available in PDF, EPUB and Kindle. This volume originated in the workshop held at Nagoya University, August 28–30, 2015, focusing on the surprising and mysterious Ohkawa's theorem: the Bousfield classes in the stable homotopy category SH form a set. An inspiring, extensive mathematical story can be narrated starting with Ohkawa's theorem, evolving naturally with a chain of motivational questions: Ohkawa's theorem states that the Bousfield classes of the stable homotopy category SH surprisingly forms a set, which is still very mysterious. Are there any toy models where analogous Bousfield classes form a set with a clear meaning? The fundamental theorem of Hopkins, Neeman, Thomason, and others states that the analogue of the Bousfield classes in the derived category of quasi-coherent sheaves Dqc(X) form a set with a clear algebro-geometric description. However, Hopkins was actually motivated not by Ohkawa's theorem but by his own theorem with Smith in the triangulated subcategory SHc, consisting of compact objects in SH. Now the following questions naturally occur: (1) Having theorems of Ohkawa and Hopkins-Smith in SH, are there analogues for the Morel-Voevodsky A1-stable homotopy category SH(k), which subsumes SH when k is a subfield of C?, (2) Was it not natural for Hopkins to have considered Dqc(X)c instead of Dqc(X)? However, whereas there is a conceptually simple algebro-geometrical interpretation Dqc(X)c = Dperf(X), it is its close relative Dbcoh(X) that traditionally, ever since Oka and Cartan, has been intensively studied because of its rich geometric and physical information. This book contains developments for the rest of the story and much more, including the chromatics homotopy theory, which the Hopkins–Smith theorem is based upon, and applications of Lurie's higher algebra, all by distinguished contributors.
