Bosa, J., Tornetta, G. and Zacharias, J. (2019) A bivariant theory for the Cuntz semigroup. Journal of Functional Analysis, 277(4), pp. 1061-1111. (doi: 10.1016/j.jfa.2019.05.002)
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Abstract
We introduce a bivariant version of the Cuntz semigroup as equivalence classes of order zero maps generalizing the ordinary Cuntz semigroup. The theory has many features formally analogous to KK-theory including a composition product. We establish basic properties, like additivity, stability and continuity, and study categorical aspects in the setting of local C⁎-algebras. We determine the bivariant Cuntz semigroup for numerous examples such as when the second algebra is a Kirchberg algebra, and Cuntz homology for compact Hausdorff spaces which provides a complete invariant. Moreover, we establish identities when tensoring with strongly self-absorbing C⁎-algebras. Finally, we show how to use the bivariant Cuntz semigroup of the present work to classify unital and stably finite C⁎-algebras.
Item Type: | Articles |
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Additional Information: | This research was also supported by Juan de la Cierva - Incorporacio ́n (IJCI2015-25237) and is partially supported by the project MTM2014-53644-P |
Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Tornetta, Mr Gabriele and Bosa, Dr Joan and Zacharias, Professor Joachim |
Authors: | Bosa, J., Tornetta, G., and Zacharias, J. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Journal of Functional Analysis |
Publisher: | Elsevier |
ISSN: | 0022-1236 |
ISSN (Online): | 1096-0783 |
Published Online: | 11 May 2019 |
Copyright Holders: | Copyright © 2019 The Authors |
First Published: | First published in Journal of Functional Analysis 277(4):1061-1111 |
Publisher Policy: | Reproduced under a Creative Commons License |
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