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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


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Volume 2016, Issue 718

Issues

A Dixmier--Douady theory for strongly self-absorbing C *-algebras

Marius Dadarlat / Ulrich Pennig
  • Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstraße 62, 48149 Münster, Germany
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Published Online: 2015-03-13 | DOI: https://doi.org/10.1515/crelle-2014-0044

Abstract

We show that the Dixmier–Douady theory of continuous fields of C*-algebras with compact operators 𝕂 as fibers extends significantly to a more general theory of fields with fibers A 𝕂 where A is a strongly self-absorbing C*-algebra. The classification of the corresponding locally trivial fields involves a generalized cohomology theory which is computable via the Atiyah–Hirzebruch spectral sequence. An important feature of the general theory is the appearance of characteristic classes in higher dimensions. We also give a necessary and sufficient K-theoretical condition for local triviality of these continuous fields over spaces of finite covering dimension.

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About the article

Received: 2013-05-20

Revised: 2013-09-02

Published Online: 2015-03-13

Published in Print: 2016-09-01


Funding Source: National Science Foundation

Award identifier / Grant number: #DMS–1101305

M. Dadarlat was partially supported by NSF grant #DMS–1101305.


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2016, Issue 718, Pages 153–181, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2014-0044.

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