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.

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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: http://theses.gla.ac.uk/id/eprint/7203

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