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Author : Po Hu
Publisher :
ISBN 13 : 9782856291368
Total Pages : 108 pages
Book Rating : 4.2/5 (913 download)
Download or read book Duality for Smooth Families in Equivariant Stable Homotopy Theory written by Po Hu and published by . This book was released on 2003 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : L. Gaunce Jr. Lewis
Publisher : Springer
ISBN 13 : 3540470778
Total Pages : 548 pages
Book Rating : 4.5/5 (44 download)
Download or read book Equivariant Stable Homotopy Theory written by L. Gaunce Jr. Lewis and published by Springer. This book was released on 2006-11-14 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : J. Peter May
Publisher : American Mathematical Soc.
ISBN 13 : 0821839225
Total Pages : 456 pages
Book Rating : 4.8/5 (218 download)
Download or read book Parametrized Homotopy Theory written by J. Peter May and published by American Mathematical Soc.. This book was released on 2006 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops rigorous foundations for parametrized homotopy theory, which is the algebraic topology of spaces and spectra that are continuously parametrized by the points of a base space. It also begins the systematic study of parametrized homology and cohomology theories. The parametrized world provides the natural home for many classical notions and results, such as orientation theory, the Thom isomorphism, Atiyah and Poincare duality, transfer maps, the Adams and Wirthmuller isomorphisms, and the Serre and Eilenberg-Moore spectral sequences. But in addition to providing a clearer conceptual outlook on these classical notions, it also provides powerful methods to study new phenomena, such as twisted $K$-theory, and to make new constructions, such as iterated Thom spectra. Duality theory in the parametrized setting is particularly illuminating and comes in two flavors. One allows the construction and analysis of transfer maps, and a quite different one relates parametrized homology to parametrized cohomology. The latter is based formally on a new theory of duality in symmetric bicategories that is of considerable independent interest. The text brings together many recent developments in homotopy theory. It provides a highly structured theory of parametrized spectra, and it extends parametrized homotopy theory to the equivariant setting. The theory of topological model categories is given a more thorough treatment than is available in the literature. This is used, together with an interesting blend of classical methods, to resolve basic foundational problems that have no nonparametrized counterparts.
Author : Michael A. Hill
Publisher : Cambridge University Press
ISBN 13 : 1108831443
Total Pages : 881 pages
Book Rating : 4.1/5 (88 download)
Download or read book Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem written by Michael A. Hill and published by Cambridge University Press. This book was released on 2021-07-29 with total page 881 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete and definitive account of the authors' resolution of the Kervaire invariant problem in stable homotopy theory.
Author : Po Hu
Publisher : American Mathematical Soc.
ISBN 13 : 0821829564
Total Pages : 141 pages
Book Rating : 4.8/5 (218 download)
Download or read book $S$-Modules in the Category of Schemes written by Po Hu and published by American Mathematical Soc.. This book was released on 2003 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gives a theory $S$-modules for Morel and Voevodsky's category of algebraic spectra over an arbitrary field $k$. This work also defines universe change functors, as well as other important constructions analogous to those in topology, such as the twisted half-smash product.
Author : Christian Ausoni
Publisher : American Mathematical Soc.
ISBN 13 : 0821848399
Total Pages : 274 pages
Book Rating : 4.8/5 (218 download)
Download or read book Alpine Perspectives on Algebraic Topology written by Christian Ausoni and published by American Mathematical Soc.. This book was released on 2009 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the Third Arolla Conference on Algebraic Topology, which took place in Arolla, Switzerland, on August 18-24, 2008. This title includes research papers on stable homotopy theory, the theory of operads, localization and algebraic K-theory, as well as survey papers on the Witten genus and localization techniques.
Author : Douglas C. Ravenel
Publisher : Princeton University Press
ISBN 13 : 9780691025728
Total Pages : 228 pages
Book Rating : 4.0/5 (257 download)
Download or read book Nilpotence and Periodicity in Stable Homotopy Theory written by Douglas C. Ravenel and published by Princeton University Press. This book was released on 1992-11-08 with total page 228 pages. 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.
Author : Ralph L. Cohen
Publisher : American Mathematical Soc.
ISBN 13 : 082182242X
Total Pages : 102 pages
Book Rating : 4.8/5 (218 download)
Download or read book Odd Primary Infinite Families in Stable Homotopy Theory written by Ralph L. Cohen and published by American Mathematical Soc.. This book was released on 1981 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addresses issues with odd primary infinite families in stable homotopy theory.
Author : Peter Hilton
Publisher : Taylor & Francis Group
ISBN 13 :
Total Pages : 246 pages
Book Rating : 4.3/5 (91 download)
Download or read book Homotopy Theory and Duality written by Peter Hilton and published by Taylor & Francis Group. This book was released on 1966 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 1106 pages
Book Rating : 4.3/5 (91 download)
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1106 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. S. Milne
Publisher :
ISBN 13 :
Total Pages : 440 pages
Book Rating : 4.3/5 (97 download)
Download or read book Arithmetic Duality Theorems written by J. S. Milne and published by . This book was released on 1986 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here, published for the first time, are the complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry. The text covers these theorems in Galois cohomology, ,tale cohomology, and flat cohomology and addresses applications in the above areas. The writing is expository and the book will serve as an invaluable reference text as well as an excellent introduction to the subject.
Author : Bjorn Ian Dundas
Publisher : Springer Science & Business Media
ISBN 13 : 3540458972
Total Pages : 228 pages
Book Rating : 4.5/5 (44 download)
Download or read book Motivic Homotopy Theory written by Bjorn Ian Dundas and published by Springer Science & Business Media. This book was released on 2007-07-11 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background material from both of these fields, as well as the foundations of motivic homotopy theory. It will serve as a good introduction as well as a convenient reference for a broad group of mathematicians to this important and fascinating new subject. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject.
Author : Martin C. Olsson
Publisher :
ISBN 13 :
Total Pages : 422 pages
Book Rating : 4.F/5 ( download)
Download or read book Crystalline Cohomology of Algebraic Stacks and Hyodo-Kato Cohomology written by Martin C. Olsson and published by . This book was released on 2007 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text the author uses stack-theoretic techniques to study the crystalline structure on the de Rham cohomology of a proper smooth scheme over a $p$-adic field and applications to $p$-adic Hodge theory. He develops a general theory of crystalline cohomology and de Rham-Witt complexes for algebraic stacks and applies it to the construction and study of the $(\varphi, N, G)$-structure on de Rham cohomology. Using the stack-theoretic point of view instead of log geometry, he develops the ingredients needed to prove the $C_{\text {st}}$-conjecture using the method of Fontaine, Messing, Hyodo, Kato, and Tsuji, except for the key computation of $p$-adic vanishing cycles. He also generalizes the construction of the monodromy operator to schemes with more general types of reduction than semistable and proves new results about tameness of the action of Galois on cohomology.
Author : Zev Rosengarten
Publisher : American Mathematical Society
ISBN 13 : 1470467070
Total Pages : 230 pages
Book Rating : 4.4/5 (74 download)
Download or read book Tate Duality in Positive Dimension over Function Fields written by Zev Rosengarten and published by American Mathematical Society. This book was released on 2023-11-27 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Author : Kristian J. Moi
Publisher :
ISBN 13 : 9788770789707
Total Pages : pages
Book Rating : 4.7/5 (897 download)
Download or read book Equivariant Homotopy Theory and K-theory of Exact Categories with Duality written by Kristian J. Moi and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Xiaonan Ma
Publisher :
ISBN 13 :
Total Pages : 172 pages
Book Rating : 4.:/5 (318 download)
Download or read book Bergman Kernels and Symplectic Reduction written by Xiaonan Ma and published by . This book was released on 2008 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors generalize several recent results concerning the asymptotic expansions of Bergman kernels to the framework of geometric quantization and establish an asymptotic symplectic identification property. More precisely, they study the asymptotic expansion of the $G$-invariant Bergman kernel of the $\mathrm{spin}^c$ Dirac operator associated with high tensor powers of a positive line bundle on a symplectic manifold admitting a Hamiltonian action of a compact connected Lie group $G$. The authors also develop a way to compute the coefficients of the expansion, and compute the first few of them; especially, they obtain the scalar curvature of the reduction space from the $G$-invariant Bergman kernel on the total space. These results generalize the corresponding results in the non-equivariant setting, which have played a crucial role in the recent work of Donaldson on stability of projective manifolds, to the geometric quantization setting. As another kind of application, the authors establish some Toeplitz operator type properties in semi-classical analysis in the framework of geometric quantization. The method used is inspired by Local Index Theory, especially by the analytic localization techniques developed by Bismut and Lebeau.
Author : Birgit Richter
Publisher : Cambridge University Press
ISBN 13 : 1108847625
Total Pages : 402 pages
Book Rating : 4.1/5 (88 download)
Download or read book From Categories to Homotopy Theory written by Birgit Richter and published by Cambridge University Press. This book was released on 2020-04-16 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topology and algebra. The reader is first introduced to category theory, starting with basic definitions and concepts before progressing to more advanced themes. Concrete examples and exercises illustrate the topics, ranging from colimits to constructions such as the Day convolution product. Part II covers important applications of category theory, giving a thorough introduction to simplicial objects including an account of quasi-categories and Segal sets. Diagram categories play a central role throughout the book, giving rise to models of iterated loop spaces, and feature prominently in functor homology and homology of small categories.
