K-Theory for Operator Algebras (Mathematical Sciences Research Institute Publications) [Paperback]

Bruce Blackadar (Author)

Book Description

Publication Date: September 13, 1998 | ISBN-10: 0521635322 | ISBN-13: 978-0521635325 | Edition: Revised

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-theory for operator algebras, and is intended to help students, non specialists, and specialists learn the subject. This first paperback printing has been revised and expanded and contains an updated reference list. This book develops K-theory, the theory of extensions, and Kasparov's bivariant KK-theory for C*-algebras. Special topics covered include the theory of AF algebras, axiomatic K-theory, the Universal Coefficient Theorem, and E-theory. Although the book is technically complete, motivation and intuition are emphasized. Many examples and applications are discussed.

Editorial Reviews

Review

"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

Book Description

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-theory for operator algebras, and is intended to help students, non-specialists, and specialists learn the subject. This first paperback printing has been revised and expanded and contains an updated reference list.

Product Details

• Paperback: 324 pages
• Publisher: Cambridge University Press; Revised edition (September 13, 1998)
• Language: English
• ISBN-10: 0521635322
• ISBN-13: 978-0521635325
• Product Dimensions: 8.8 x 6 x 1.1 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,830,130 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

9 of 9 people found the following review helpful:

5.0 out of 5 stars A difficult book on a difficult subject, May 1, 1999

By 

[e-mail] (Hamburg, Germany) - See all my reviews

This review is from: K-Theory for Operator Algebras (Mathematical Sciences Research Institute Publications) (Paperback)

The books covers not only K-theory but also KK-theory that was introduced by G. G. Kasparov. The original article by Kasparov are very hard to read because of the generality of his approach. Furthermore the theory was much simplified by Skandalis et al. The second part of the book offers a very readable introduction to KK-theory. Now the new edition even contains a short exposition of E-theory.

"Elements of KK-theory" by K. K. Jensen and K. Thomsen is good introduction too.

8 of 8 people found the following review helpful:

5.0 out of 5 stars A well-written book on a difficult subject, December 24, 2001

By 

Yonatan Zunger (Mountain View, CA USA) - See all my reviews
(REAL NAME)   

This review is from: K-Theory for Operator Algebras (Mathematical Sciences Research Institute Publications) (Paperback)

K-theory is a challenging subject; Kasparov's KK-theory even more so. But Bruce Blackadar's textbook manages to present both of these in a clear and coherent fashion, readable both by mathematicians and physicists. The ideal reader of this book will already be familiar with the basics of operator algebras and will have had some exposure to K-theory (perhaps through Wegge-Olsen's remarkable book) and noncommutative geometry; but an extensive background is not needed.

One especially good feature of this book is the wealth of examples it contains, especially those examples of most relevance to string theory. (Where K-theory is finding some of its most interesting applications today) A wide range of subjects such as "topological" K-theory (the K-theory of gauge fields) and supersymmetry (referred to as "grading," following mathematicians' notation) round out this presentation of one of the most exciting subjects on the border of mathematics and physics.