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.
Publisher: Springer-Verlag New York Inc.
Number of pages: 337
Weight: 533 g
Dimensions: 235 x 155 x 18 mm
Edition: Softcover reprint of the original 1st ed. 198
"This book gives a comprehensive survey of 'operator' K-theory or 'noncommutative' algebraic topology. Since its inception in the early 1970s, the field has grown rapidly, until a deep and elaborate machinery has evolved. This book is the first to consolidate this material and does an excellent job of presenting the path of least resistance to the key results while keeping the reader informed about the many important sidetracks." Mathematical Reviews
'The book is well written, with a great number of examples, exercises and problems that help one to understand the theory ...'. European Maths Society Journal