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

Dadarlat, Marius; Pennig, Ulrich

doi:10.2140/agt.2015.15.137

¹Department of Mathematics, Purdue University, 150 N University Street, West Lafayette, IN 47907-2067, USA
²Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstraße 62, D-48149 Münster, Germany

Algebraic and Geometric Topology, Tome 15 (2015) no. 1, pp. 137-168

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Résumé

We give an operator algebraic model for the first group of the unit spectrum gl1(KU) of complex topological K–theory, ie [X,BGL1(KU)], by bundles of stabilized infinite Cuntz C∗–algebras O∞⊗ 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.

DOI : 10.2140/agt.2015.15.137

Classification : 46L80, 55P42
Keywords: unit spectrum, topological $K$–theory, twisted $K$–theory, strongly self-absorbing $C^*$–algebra, ring spectrum

Affiliations des auteurs :

Dadarlat, Marius ¹ ; Pennig, Ulrich ²

¹ Department of Mathematics, Purdue University, 150 N University Street, West Lafayette, IN 47907-2067, USA
² Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstraße 62, D-48149 Münster, Germany

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Dadarlat, Marius; Pennig, Ulrich. Unit spectra of K–theory from strongly self-absorbing C∗–algebras. Algebraic and Geometric Topology, Tome 15 (2015) no. 1, pp. 137-168. doi: 10.2140/agt.2015.15.137

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