K THEORY

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Algebraic K Theory

Author : Vasudevan Srinivas
ISBN : 9781489967350
Genre : Juvenile Nonfiction
File Size : 73.60 MB
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Category: Juvenile Nonfiction

Algebraic K Theory And Its Applications

Author : Jonathan Rosenberg
ISBN : 9781461243144
Genre : Mathematics
File Size : 58.17 MB
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Algebraic K-Theory is crucial in many areas of modern mathematics, especially algebraic topology, number theory, algebraic geometry, and operator theory. This text is designed to help graduate students in other areas learn the basics of K-Theory and get a feel for its many applications. Topics include algebraic topology, homological algebra, algebraic number theory, and an introduction to cyclic homology and its interrelationship with K-Theory.
Category: Mathematics

Topological And Bivariant K Theory

Author : Joachim Cuntz
ISBN : 9783764383992
Genre : Mathematics
File Size : 71.92 MB
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Topological K-theory is one of the most important invariants for noncommutative algebras. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic K-theory. This book describes a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, it details other approaches to bivariant K-theories for operator algebras. The book studies a number of applications, including K-theory of crossed products, the Baum-Connes assembly map, twisted K-theory with some of its applications, and some variants of the Atiyah-Singer Index Theorem.
Category: Mathematics

Algebraic K Theory Connections With Geometry And Topology

Author : John Jardine
ISBN : 0792302923
Genre : Mathematics
File Size : 33.5 MB
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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.
Category: Mathematics

An Introduction To K Theory For C Algebras

Author : M. Rørdam
ISBN : 0521789443
Genre : Mathematics
File Size : 44.65 MB
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This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.
Category: Mathematics

K Theory Of Forms

Author : Anthony Bak
ISBN : 0691082758
Genre : Mathematics
File Size : 27.64 MB
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The Description for this book, K-Theory of Forms. (AM-98), will be forthcoming.
Category: Mathematics

K Theory For Operator Algebras

Author : Bruce Blackadar
ISBN : 0521635322
Genre : Mathematics
File Size : 23.98 MB
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This book is the only comprehensive treatment of K-theory for operator algebras.
Category: Mathematics

Complex Topological K Theory

Author : Efton Park
ISBN : 9781139469746
Genre : Mathematics
File Size : 38.3 MB
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Topological K-theory is a key tool in topology, differential geometry and index theory, yet this is the first contemporary introduction for graduate students new to the subject. No background in algebraic topology is assumed; the reader need only have taken the standard first courses in real analysis, abstract algebra, and point-set topology. The book begins with a detailed discussion of vector bundles and related algebraic notions, followed by the definition of K-theory and proofs of the most important theorems in the subject, such as the Bott periodicity theorem and the Thom isomorphism theorem. The multiplicative structure of K-theory and the Adams operations are also discussed and the final chapter details the construction and computation of characteristic classes. With every important aspect of the topic covered, and exercises at the end of each chapter, this is the definitive book for a first course in topological K-theory.
Category: Mathematics

Topics In Algebraic And Topological K Theory

Author : Paul Frank Baum
ISBN : 9783642157073
Genre : Mathematics
File Size : 89.80 MB
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This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within the field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparison between algebraic and topological K-theory of topological algebras, the K-theory of schemes, and the theory of dg-categories.
Category: Mathematics

Handbook Of K Theory

Author : Eric Friedlander
ISBN : 9783540230199
Genre : Mathematics
File Size : 70.74 MB
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This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.
Category: Mathematics