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arXiv · 2302.08028

Computing cohomology groups that classify bundles of strongly self-absorbing $C^*$-algebras

Marius Dadarlat·James E. McClure·Ulrich Pennig
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Abstract

Locally trivial bundles of $C^*$-algebras with fibre $D \otimes \mathcal{K}$ for a strongly self-absorbing $C^*$-algebra $D$ over a finite CW-complex $X$ form a group $E^1_D(X)$ that is the first group of a cohomology theory $E^*_D(X)$. In this paper we compute these groups by expressing them in terms of ordinary cohomology and connective $K$-theory. To compare the $C^*$-algebraic version of $gl_1(KU)$ with its classical counterpart we also develop a uniqueness result for the unit spectrum of complex periodic topological $K$-theory.

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Marius Dadarlat, James E. McClure, Ulrich Pennig. 2023-02-16. Computing cohomology groups that classify bundles of strongly self-absorbing $C^*$-algebras. https://doi.org/10.1142/s1793525324500110

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