Operator Algebras and Applications: Volume 1, Structure Theory; K-theory, Geometry and Topology - 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 Operator Algebras and Applications: Volume 1, Structure Theory; K-theory, Geometry and Topology write by David E. Evans. This book was released on 1988. Operator Algebras and Applications: Volume 1, Structure Theory; K-theory, Geometry and Topology available in PDF, EPUB and Kindle. These volumes form an authoritative statement of the current state of research in Operator Algebras. They consist of papers arising from a year-long symposium held at the University of Warwick. Contributors include many very well-known figures in the field.
Operator Algebras and Applications
Operator Algebras and Applications - 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 Operator Algebras and Applications write by David E. Evans. This book was released on 1989. Operator Algebras and Applications available in PDF, EPUB and Kindle. These volumes form an authoritative statement of the current state of research in Operator Algebras. They consist of papers arising from a year-long symposium held at the University of Warwick. Contributors include many very well-known figures in the field.
K-Theory for Operator Algebras
K-Theory for Operator Algebras - 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 K-Theory for Operator Algebras write by Bruce Blackadar. This book was released on 2012-12-06. K-Theory for Operator Algebras available in PDF, EPUB and Kindle. K -Theory has revolutionized the study of operator algebras in the last few years. As the primary component of the subject of "noncommutative topol ogy," K -theory has opened vast new vistas within the structure theory of C* algebras, as well as leading to profound and unexpected applications of opera tor algebras to problems in geometry and topology. As a result, many topolo gists and operator algebraists have feverishly begun trying to learn each others' subjects, and it appears certain that these two branches of mathematics have become deeply and permanently intertwined. Despite the fact that the whole subject is only about a decade old, operator K -theory has now reached a state of relative stability. While there will undoubtedly be many more revolutionary developments and applications in the future, it appears the basic theory has more or less reached a "final form." But because of the newness of the theory, there has so far been no comprehensive treatment of the subject. It is the ambitious goal of these notes to fill this gap. We will develop the K -theory of Banach algebras, the theory of extensions of C*-algebras, and the operator K -theory of Kasparov from scratch to its most advanced aspects. We will not treat applications in detail; however, we will outline the most striking of the applications to date in a section at the end, as well as mentioning others at suitable points in the text.
Operator Algebras and Applications: Volume 1, Structure Theory; K-theory, Geometry and Topology
Operator Algebras and Applications: Volume 1, Structure Theory; K-theory, Geometry and Topology - 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 Operator Algebras and Applications: Volume 1, Structure Theory; K-theory, Geometry and Topology write by David E. Evans. This book was released on 2010-07-06. Operator Algebras and Applications: Volume 1, Structure Theory; K-theory, Geometry and Topology available in PDF, EPUB and Kindle. These volumes form an authoritative statement of the current state of research in Operator Algebras. They consist of papers arising from a year-long symposium held at the University of Warwick. Contributors include many very well-known figures in the field.
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.
