KKtheory

General Introduction
See also BaumSchneider cohomology
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Search results
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Online References
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Paper References
Jensen and Thomsen: Elements of KKtheory (book)
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
On the KKtheory and the Etheory of amalgamated free products of C*algebras, by Klaus Thomsen: K0472
Title: Unbounded bivariant $K$theory and correspondences in noncommutative geometry Authors: Bram Mesland http://front.math.ucdavis.edu/0904.4383 Categories: math.KT KTheory and Homology (math.OA Operator Algebras) Comments: 67 pages. Final version. Accepted for publication MSC: 46L80 Abstract: By introducing a notion of smooth connection for unbounded $KK$cycles, we show that the Kasparov product of such cycles can be defined directly, by an algebraic formula. In order to achieve this it is necessary to develop a framework of smooth algebras and a notion of differentiable $C^{*}$module. The theory of operator spaces provides the required tools. Finally, the above mentioned $KK$cycles with connection can be viewed as the morphisms in a category whose objects are spectral triples.
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Other Information
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