Unit spectra of K-theory from strongly self-absorbing C*-algebras

Dadarlat, Marius and Pennig, Ulrich ORCID: https://orcid.org/0000-0001-5441-6130 2015. Unit spectra of K-theory from strongly self-absorbing C*-algebras. Algebraic and Geometric Topology 15 (1) , pp. 137-168. 10.2140/agt.2015.15.137

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Abstract

We give an operator algebraic model for the first group of the unit spectrum gl_1(KU) of complex topological K-theory, i.e. [X,BGL_1(KU)], by bundles of stabilized infinite Cuntz C*-algebras O_{\infty} \otimes \K. We develop similar models for the localizations of KU at a prime p and away from p. Our work is based on the I-monoid model for the units of K-theory by Sagave and Schlichtkrull and it was motivated by the goal of finding connections between the infinite loop space structure of the classifying space of the automorphism group of stabilized strongly self-absorbing C*-algebras that arose in our generalization of the Dixmier-Douady theory and classical spectra from algebraic topology.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Mathematical Sciences Publishers (MSP)
ISSN:	1472-2747
Date of First Compliant Deposit:	2 December 2016
Date of Acceptance:	21 July 2014
Last Modified:	15 Nov 2024 08:45
URI:	https://orca.cardiff.ac.uk/id/eprint/89484

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