A bivariant theory for the Cuntz semigroup and its role for the classification programme of C*-algebras

[摘要] A bivariant theory for the Cuntz semigroup is introduced and analysed. This is used to define a Cuntz-analogue of K-homology, which turns out to provide a complete invariant for compact Hausdorff spaces. Furthermore, a classification result for the class of unital and stably finite C*-algebras is proved, which can be considered as a formal analogue of the Kirchberg-Phillips classification result for purely infinite C*-algebras by means ofKK-theory, i.e. bivariant K-theory.An equivariant extension of the bivariant Cuntz semigroup proposed in this thesis is also presented, and some well-known classification results are derived within this new theory, thus showing that it can be applied successfully to the problem of classification of some actions by compact groups over certain C*-algebras of the stably finite type.

[发布机构] University:University of Glasgow;Department:School of Mathematics and Statistics

[关键词] Functional analysis, operator algebras, classification of C*-algebras, dynamical systems, K-theory, KK-theory, K-homology, Cuntz semigroup, non-commutative topology.