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Title: K-Theory for Operator Algebras by Bruce Blackadar ISBN: 0-521-63532-2 Publisher: Cambridge University Press Pub. Date: 01 December, 1998 Format: Paperback Volumes: 1 List Price(USD): $37.00 |
Average Customer Rating: 5 (2 reviews)
Rating: 5
Summary: A well-written book on a difficult subject
Comment: 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.
Rating: 5
Summary: A difficult book on a difficult subject
Comment: 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.
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Title: An Introduction to K-Theory for C*-Algebras by M. Rrdam, F. Larsen, N. Laustsen, M. Rordam ISBN: 0521789443 Publisher: Cambridge University Press Pub. Date: 01 September, 2000 List Price(USD): $32.00 |
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Title: Algebraic Topology by Marvin J. Greenberg ISBN: 0805335579 Publisher: Benjamin-Cummings Publishing Company Pub. Date: 01 February, 1982 List Price(USD): $32.75 |
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Title: Noncommutative Geometry by Alain Connes ISBN: 012185860X Publisher: Academic Press Pub. Date: 01 December, 1994 List Price(USD): $81.95 |
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Title: Undergraduate Algebraic Geometry by M. Reid ISBN: 0521356628 Publisher: Cambridge University Press Pub. Date: 01 April, 1988 List Price(USD): $19.00 |
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Title: Topology, Geometry, and Gauge Fields: Foundations by Gregory L. Naber ISBN: 0387949461 Publisher: Springer-Verlag Telos Pub. Date: 15 January, 1997 List Price(USD): $64.95 |
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