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An Introduction to K-Theory for C*-Algebras

An Introduction to K-Theory for C*-Algebras more books like this

by F Larsen, M Rrdam, M Rordam

Over the last 25 years K-theory has become an integrated part of the study of C*-algebras. This book gives an elementary introduction to this interesting and rapidly growing area of mathematics. Fundamental to K-theory is the association of a pair of Abelian groups, K0(A) and K1(A), to each C*-algebra A. These groups reflect the properties of A in ...

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Algebraic Topology and Algebraic K-Theory: Proceedings of a Symposium in Honor of John C. Moore. (Am-113)

Algebraic Topology and Algebraic K-Theory: Proceedings of a Symposium in Honor of John C. Moore. (Am-113) more books like this

by William Browder (Editor), John C Moore

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Algebraic K-Theory and Its Applications

Algebraic K-Theory and Its Applications more books like this

by Jonathan Rosenberg

Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. The broad range of these topics has tended to give the subject an aura of inapproachability. This book, based on a course at the University of Maryland in the ...

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The Classical Groups and K-Theory

The Classical Groups and K-Theory more books like this

by Alexander Hahn

This book gives a comprehensive account of the basic algebraic properties of the classical groups over rings. Much of the theory appears in book form for the first time, and most proofs are given in detail. The book also includes a revised and expanded version of Dieudonne's classical theory over division rings. The authors analyse congruence ...

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Lower K-& L-Theory

Lower K-& L-Theory more books like this

by Andrew Ranicki

This is the first unified treatment in book form of the lower K-groups of Bass and the lower L-groups of the author. These groups arise as the Grothendieck groups of modules and quadratic forms which are components of the K- and L-groups of polynomial extensions. They are important in the topology of non-compact manifolds such as Euclidean spaces, ...

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The Novikov Conjecture: Geometry and Algebra

The Novikov Conjecture: Geometry and Algebra more books like this

by Matthias Kreck

These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They begin with basics about higher signatures, Whitehead torsion and the s-Cobordism Theorem. Then an introduction to surgery theory and a version of the assembly map is presented. Using the solution of the ...

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K-Theory

K-Theory more books like this

by Michael Francis Atiyah

These notes are based on the course of lectures I gave at Harvard in the fall of 1964. They constitute a self-contained account of vector bundles and K-theory assuming only the rudiments of point-set topology and linear algebra. One of the features of the treatment is that no use is made of ordinary homology or cohomology theory. In fact, ...

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Topics in Cohomological Studies of Algebraic Varieties: Impanga Lecture Notes

Topics in Cohomological Studies of Algebraic Varieties: Impanga Lecture Notes more books like this

by Piotr Pragacz

The articles in this volume study various cohomological aspects of algebraic varieties: characteristic classes of singular varieties; geometry of flag varieties; cohomological computations for homogeneous spaces; K-theory of algebraic varieties; quantum cohomology and Gromov-Witten theory. The main purpose is to give comprehensive introductions to ...

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K-Theory of Forms

K-Theory of Forms more books like this

by Anthony Bak

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C*-Algebra Extensions and K-Homology

C*-Algebra Extensions and K-Homology more books like this

by Ronald G Douglas

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Basic Bundle Theory and K-Cohomology Invariants more books like this

by Dale Husemoller, Michael Joachim, Branislav Jurco

Based on several recent courses given to mathematical physics students, this volume is an introduction to bundle theory with the aim to provide newcomers to the field with solid foundations in topological K-theory. A fundamental theme, emphasized in the book, centers around the gluing of local bundle data related to bundles into a global object. ...

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Asymptotic Cyclic Cohomology more books like this

by Michael Puschnigg

The aim of cyclic cohomology theories is the approximation of K-theory by cohomology theories defined by natural chain complexes. The basic example is the approximation of topological K-theory by de Rham cohomology via the classical Chern character. A cyclic cohomology theory for operator algebras is developed in the book, based on Connes' work on ...

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Topological and Bivariant K-Theory more books like this

by Joachim Cuntz, Ralf Meyer, Jonathan M Rosenberg

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 ...

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Complex Topological K-Theory more books like this

by Efton Park

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 ...

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Representation Theory and Higher Algebraic K-Theory more books like this

by Aderemi Kuku

"Representation Theory and Higher Algebraic K-Theory" is the first book to present higher algebraic K-theory of orders and group rings as well as characterize higher algebraic K-theory as Mackey functors that lead to equivariant higher algebraic K-theory and their relative generalizations. Thus, this book makes computations of higher K-theory of ...

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The relation of cobordism to k-theories more books like this

by P. E. Conner, E. E. Floyd

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K-theory of finite groups and orders more books like this

by Richard G Swan, Graham E Evans (Notes by)

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K-Theory: An Introduction more books like this

by Max Karoubi

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Cyclic Cohomology and Noncommutative Geometry more books like this

by Joachim J R Cuntz

Noncommutative geometry is a new field that is among the great challenges of present-day mathematics. Its methods allow one to treat noncommutative algebras - such as algebras of pseudodifferential operators, group algebras, or algebras arising from quantum field theory - on the same footing as commutative algebras, that is, as spaces. The ...

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General cohomology theory and K-theory more books like this

by Peter John Hilton, J W S Cassels (Editor), N J Hitchin (Editor)

These notes constitute a faithful record of a short course of lectures given in Sao Paulo, Brazil, in the summer of 1968. The audience was assumed to be familiar with the basic material of homology and homotopy theory, and the object of the course was to explain the methodology of general cohomology theory and to give applications of K-theory to ...

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K-Theory and C*-Algebras: A Friendly Approach more books like this

by N E Wegge-Olsen

K-theory is often considered a complicated 'specialist's' theory. This book is an introduction to the basics and provides detailed explanation of the various concepts required for a deeper understanding of the subject. Some familiarity with basic C*algebra theory is assumed and then follows a careful construction and analysis of the operator K ...

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K-theory for operator algebras more books like this

by Blackadar

K-theory has helped convert the theory of operator algebras from a simple branch of functional analysis to a subject with broad applicability throughout mathematics, especially in geometry and topology, and many mathematicians of diverse backgrounds must learn the essential parts of the theory. This book is the only comprehensive treatment of K ...

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Valuations, Orderings, and Milnor K-Theory more books like this

by Ido Efrat

This monograph is a comprehensive exposition of the modern theory of valued and ordered fields. It presents the classical aspects of such fields: their arithmetic, topology, and Galois theory. Deeper cohomological aspects are studied in its last part in an elementary manner. This is done by means of the newly developed theory of generalized Milnor ...

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Skew Fields more books like this

by Draxl

The book is written in three parts. Part I consists of preparatory work on algebras, needed in Parts II and III. This material is presented in a classical, though unusual, way. Part II consists of a modern description of the theory of Brauer groups over fields (from as elementary a point of view as possible). Part III covers some new developments ...

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Algebraic K-Theory more books like this

by Robert W. Thomason, Victor P. Snaith (Editor)

This conference proceedings volume is produced in connection with the second Great Lakes K-theory Conference that was held at The Fields Institute for Research in Mathematical Sciences in March 1996. The volume is dedicated to the late Bob Thomason, one of the leading research mathematicians specializing in algebraic K-theory. In addition to ...

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