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Author : Victor Percy Snaith
Publisher :
ISBN 13 : 9781470406905
Total Pages : 102 pages
Book Rating : 4.4/5 (69 download)
Download or read book Algebraic K-theory and Localised Stable Homotopy Theory written by Victor Percy Snaith and published by . This book was released on 1983 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : William Browder
Publisher : Princeton University Press
ISBN 13 : 1400882117
Total Pages : 567 pages
Book Rating : 4.4/5 (8 download)
Download or read book Algebraic Topology and Algebraic K-Theory (AM-113), Volume 113 written by William Browder and published by Princeton University Press. This book was released on 2016-03-02 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains accounts of talks held at a symposium in honor of John C. Moore in October 1983 at Princeton University, The work includes papers in classical homotopy theory, homological algebra, rational homotopy theory, algebraic K-theory of spaces, and other subjects.
Author : William Browder
Publisher : Princeton University Press
ISBN 13 : 0691084262
Total Pages : 576 pages
Book Rating : 4.6/5 (91 download)
Download or read book Algebraic Topology and Algebraic K-theory written by William Browder and published by Princeton University Press. This book was released on 1987-11-21 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains accounts of talks held at a symposium in honor of John C. Moore in October 1983 at Princeton University, The work includes papers in classical homotopy theory, homological algebra, rational homotopy theory, algebraic K-theory of spaces, and other subjects.
Author : Bjørn Ian Dundas
Publisher : Springer Science & Business Media
ISBN 13 : 1447143930
Total Pages : 447 pages
Book Rating : 4.4/5 (471 download)
Download or read book The Local Structure of Algebraic K-Theory written by Bjørn Ian Dundas and published by Springer Science & Business Media. This book was released on 2012-09-06 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Andrea Basantes-Andrade
Publisher : Springer
ISBN 13 : 9783030372200
Total Pages : 479 pages
Book Rating : 4.3/5 (722 download)
Download or read book Technology, Sustainability and Educational Innovation (TSIE) written by Andrea Basantes-Andrade and published by Springer. This book was released on 2020-01-04 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of International Conference on Knowledge Society: Technology, Sustainability and Educational Innovation (TSIE 2019). The conference, which was held at UTN in Ibarra, Ecuador, on 3–5 July 2019, allowed participants and speakers to share their research and findings on emerging and innovative global issues. The conference was organized in collaboration with a number of research groups: Group for the Scientific Research Network (e-CIER); Research Group in Educational Innovation and Technology, University of Salamanca, Spain(GITE-USAL); International Research Group for Heritage and Sustainability (GIIPS), and the Social Science Research Group (GICS). In addition, it had the endorsement of the RedCLARA, e-science, Fidal Foundation, Red CEDIA, IEEE, Microsoft, Business IT, Adobe, and Argo Systems. The term “knowledge society” can be understood as the management, understanding and co-creation of knowledge oriented toward the sustainable development and positive transformation of society. In this context and on the occasion of the XXXIII anniversary of the Universidad Técnica del Norte (UTN), the Postgraduate Institute through its Master of Technology and Educational Innovation held the I International Congress on Knowledge Society: Technology, Sustainability and Educational Innovation – TSIE 2019, which brought together educators, researchers, academics, students, managers, and professionals, from both the public and private sectors to share knowledge and technological developments. The book covers the following topics: 1. curriculum, technology and educational innovation; 2. media and education; 3. applied computing; 4. educational robotics. 5. technology, culture, heritage, and tourism development perspectives; and 6. biodiversity and sustainability.
Author : Vasudevan Srinivas
Publisher : Springer Science & Business Media
ISBN 13 : 1489967354
Total Pages : 328 pages
Book Rating : 4.4/5 (899 download)
Download or read book Algebraic K-Theory written by Vasudevan Srinivas and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : John F. Jardine
Publisher :
ISBN 13 : 9781493923014
Total Pages : pages
Book Rating : 4.9/5 (23 download)
Download or read book Local Homotopy Theory written by John F. Jardine and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph on the homotopy theory of topologized diagrams of spaces and spectra gives an expert account of a subject at the foundation of motivic homotopy theory and the theory of topological modular forms in stable homotopy theory. Beginning with an introduction to the homotopy theory of simplicial sets and topos theory, the book covers core topics such as the unstable homotopy theory of simplicial presheaves and sheaves, localized theories, cocycles, descent theory, non-abelian cohomology, stacks, and local stable homotopy theory. A detailed treatment of the formalism of the subject is interwoven with explanations of the motivation, development, and nuances of ideas and results. The coherence of the abstract theory is elucidated through the use of widely applicable tools, such as Barr's theorem on Boolean localization, model structures on the category of simplicial presheaves on a site, and cocycle categories. A wealth of concrete examples convey the vitality and importance of the subject in topology, number theory, algebraic geometry, and algebraic K-theory. Assuming basic knowledge of algebraic geometry and homotopy theory, Local Homotopy Theory will appeal to researchers and advanced graduate students seeking to understand and advance the applications of homotopy theory in multiple areas of mathematics and the mathematical sciences.
Author : Anthony D. Elmendorf
Publisher : American Mathematical Soc.
ISBN 13 : 0821843036
Total Pages : 265 pages
Book Rating : 4.8/5 (218 download)
Download or read book Rings, Modules, and Algebras in Stable Homotopy Theory written by Anthony D. Elmendorf and published by American Mathematical Soc.. This book was released on 1997 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a new point-set level approach to stable homotopy theory that has already had many applications and promises to have a lasting impact on the subject. Given the sphere spectrum $S$, the authors construct an associative, commutative, and unital smash product in a complete and cocomplete category of ``$S$-modules'' whose derived category is equivalent to the classical stable homotopy category. This construction allows for a simple and algebraically manageable definition of ``$S$-algebras'' and ``commutative $S$-algebras'' in terms of associative, or associative and commutative, products $R\wedge SR \longrightarrow R$. These notions are essentially equivalent to the earlier notions of $A {\infty $ and $E {\infty $ ring spectra, and the older notions feed naturally into the new framework to provide plentiful examples. There is an equally simple definition of $R$-modules in terms of maps $R\wedge SM\longrightarrow M$. When $R$ is commutative, the category of $R$-modules also has a
Author : John F. Jardine
Publisher : Springer Science & Business Media
ISBN 13 : 9400923996
Total Pages : 563 pages
Book Rating : 4.4/5 (9 download)
Download or read book Algebraic K-Theory: Connections with Geometry and Topology written by John F. Jardine and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: A NATO Advanced Study Institute entitled "Algebraic K-theory: Connections with Geometry and Topology" was held at the Chateau Lake Louise, Lake Louise, Alberta, Canada from December 7 to December 11 of 1987. This meeting was jointly supported by NATO and the Natural Sciences and Engineering Research Council of Canada, and was sponsored in part by the Canadian Mathematical Society. This book is the volume of proceedings for that meeting. Algebraic K-theory is essentially the study of homotopy invariants arising from rings and their associated matrix groups. More importantly perhaps, the subject has become central to the study of the relationship between Topology, Algebraic Geometry and Number Theory. It draws on all of these fields as a subject in its own right, but it serves as well as an effective translator for the application of concepts from one field in another. The papers in this volume are representative of the current state of the subject. They are, for the most part, research papers which are primarily of interest to researchers in the field and to those aspiring to be such. There is a section on problems in this volume which should be of particular interest to students; it contains a discussion of the problems from Gersten's well-known list of 1973, as well as a short list of new problems.
Author : Mark E. Mahowald
Publisher : American Mathematical Soc.
ISBN 13 : 0821808052
Total Pages : 394 pages
Book Rating : 4.8/5 (218 download)
Download or read book Homotopy Theory via Algebraic Geometry and Group Representations written by Mark E. Mahowald and published by American Mathematical Soc.. This book was released on 1998 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: The academic year 1996-97 was designated as a special year in Algebraic Topology at Northwestern University (Evanston, IL). In addition to guest lecturers and special courses, an international conference was held entitled "Current trends in algebraic topology with applications to algebraic geometry and physics". The series of plenary lectures included in this volume indicate the great breadth of the conference and the lively interaction that took place among various areas of mathematics. Original research papers were submitted, and all submissions were refereed to the usual journal standards.
Author : Charles A. Weibel
Publisher : American Mathematical Soc.
ISBN 13 : 0821891324
Total Pages : 634 pages
Book Rating : 4.8/5 (218 download)
Download or read book The $K$-book written by Charles A. Weibel and published by American Mathematical Soc.. This book was released on 2013-06-13 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Informally, $K$-theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vector spaces and producing important intrinsic invariants which are useful in the study of algebr
Author : William G. Dwyer
Publisher : American Mathematical Soc.
ISBN 13 : 0821808249
Total Pages : 326 pages
Book Rating : 4.8/5 (218 download)
Download or read book Stable and Unstable Homotopy written by William G. Dwyer and published by American Mathematical Soc.. This book was released on 1998 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of workshops on stable homotopy theory and on unstable homotopy theory held at The Field Institute as part of the homotopy program for the year 1996. The papers in the volume describe current research in the subject, and all included works were refereed. Rather than being a summary of work to be published elsewhere, each paper is the unique source for the new material it contains. The book contains current research from international experts in the subject area, and presents open problems with directions for future research.
Author : John Frank Adams
Publisher : University of Chicago Press
ISBN 13 : 0226005240
Total Pages : 384 pages
Book Rating : 4.2/5 (26 download)
Download or read book Stable Homotopy and Generalised Homology written by John Frank Adams and published by University of Chicago Press. This book was released on 1974 with total page 384 pages. 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.
Author : Satya Mandal
Publisher : World Scientific
ISBN 13 : 9811269408
Total Pages : 680 pages
Book Rating : 4.8/5 (112 download)
Download or read book Algebraic K-theory: The Homotopy Approach Of Quillen And An Approach From Commutative Algebra written by Satya Mandal and published by World Scientific. This book was released on 2023-06-22 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the author takes a pedagogic approach to Algebraic K-theory. He tried to find the shortest route possible, with complete details, to arrive at the homotopy approach of Quillen [Q] to Algebraic K-theory, with a simple goal to produce a self-contained and comprehensive pedagogic document in Algebraic K-theory, that is accessible to upper level graduate students. That is precisely what this book faithfully executes and achieves.The contents of this book can be divided into three parts — (1) The main body (Chapters 2-8), (2) Epilogue Chapters (Chapters 9, 10, 11) and (3) the Background and preliminaries (Chapters A, B, C, 1). The main body deals with Quillen's definition of K-theory and the K-theory of schemes. Chapters 2, 3, 5, 6, and 7 provide expositions of the paper of Quillen [Q], and chapter 4 is on agreement of Classical K-theory and Quillen K-theory. Chapter 8 is an exposition of the work of Swan [Sw1] on K-theory of quadrics.The Epilogue chapters can be viewed as a natural progression of Quillen's work and methods. These represent significant benchmarks and include Waldhausen K-theory, Negative K-theory, Hermitian K-theory, 𝕂-theory spectra, Grothendieck-Witt theory spectra, Triangulated categories, Nori-Homotopy and its relationships with Chow-Witt obstructions for projective modules. In most cases, the proofs are improvisation of methods of Quillen [Q].The background, preliminaries and tools needed in chapters 2-11, are developed in chapters A on Category Theory and Exact Categories, B on Homotopy, C on CW Complexes, and 1 on Simplicial Sets.
Author : John Greenlees
Publisher : Springer Science & Business Media
ISBN 13 : 940070948X
Total Pages : 396 pages
Book Rating : 4.4/5 (7 download)
Download or read book Axiomatic, Enriched and Motivic Homotopy Theory written by John Greenlees and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Paul Gregory Goerss
Publisher : American Mathematical Soc.
ISBN 13 : 0821832859
Total Pages : 520 pages
Book Rating : 4.8/5 (218 download)
Download or read book Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic $K$-Theory written by Paul Gregory Goerss and published by American Mathematical Soc.. This book was released on 2004 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: As part of its series of Emphasis Years in Mathematics, Northwestern University hosted an International Conference on Algebraic Topology. The purpose of the conference was to develop new connections between homotopy theory and other areas of mathematics. This proceedings volume grew out of that event. Topics discussed include algebraic geometry, cohomology of groups, algebraic $K$-theory, and $\mathbb{A 1$ homotopy theory. Among the contributors to the volume were Alejandro Adem,Ralph L. Cohen, Jean-Louis Loday, and many others. The book is suitable for graduate students and research mathematicians interested in homotopy theory and its relationship to other areas of mathematics.
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.
