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

QA Mathematics

Tornetta, Gabriele N. ; Engineering & Physical Sciences Research Council (EPSRC) ; Zacharias, Joachim

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.;   

Others  :  http://theses.gla.ac.uk/7203/1/2016tornettaphd.pdf

来源: University of Glasgow

【 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.