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

Tornetta, Gabriele N. (2016) A bivariant theory for the Cuntz semigroup and its role for the classification programme of C*-algebras. PhD thesis, University of Glasgow.

Abstract

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 of
KK-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.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: Functional analysis, operator algebras, classification of C*-algebras, dynamical systems, K-theory, KK-theory, K-homology, Cuntz semigroup, non-commutative topology.
• Subjects: Q Science > QA Mathematics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Funder's Name: Engineering & Physical Sciences Research Council (EPSRC)
• Supervisor's Name: Zacharias, Dr. Joachim
• Date of Award: 2016
• Depositing User: Mr Gabriele Tornetta
• Unique ID: glathesis:2016-7203
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 13 Apr 2016 15:41
• Last Modified: 29 Apr 2016 08:01
• URI: https://theses.gla.ac.uk/id/eprint/7203